中立型动力系统的稳定性研究
|
摘要
本论文集中研究中立型系统及切换中立型系统的主要动力学性质,并对其中一些热点子领域中的相关问题进行深入地讨论,得到比较完善而重要的结果.
介绍中立型系统及切换中立型系统的研究背景和研究现状,提供论文中常用的基本概念,基础知识和重要引理.它们是后续章节讨论的前提.
研究含有分布时滞的中立型系统(包括单分布的中立型系统和多分布时滞的中立型系统两种情形)的渐近稳定性.通过构造新的李雅谱诺夫泛函,结合矩阵分解的技巧和自由矩阵的思想方法,得到保守性较低的时滞相关的稳定性结果.数值实例验证所得结果的有效性和优越性.
研究含有非线性扰动的中立型时滞系统的渐近稳定性问题.通过构造新的扩展李雅谱诺夫泛函,结合自由矩阵的思想,并合理利用Schur补引理,得到保守性较低的时滞依赖的稳定性结论.
研究含有多时滞的中立型系统的有界输入有界输出稳定性问题.利用等价描述系统的方法,在构造李雅谱诺夫泛函过程中适当引入自由矩阵,结合矩阵分析技巧设计使得系统有界输入有界输出稳定的控制器.
讨论切换中立型系统的稳定性分析.首先,提供构造新的分段李雅普诺夫泛函,设计两种使得切换中立型系统稳定的切换规则.其中,依赖于状态的切换规则是通过求解李雅普诺夫-梅兹勒矩阵不等式而设计的,而依赖于时间的切换规则是利用平均驻留时间的方法,并结合线性矩阵不等式求解而得到的.依赖于状态的切换规则降低了现有文献设计的切换规则所带来的保守性.类似地,设计使得切换中立型扰动系统渐近稳定的切换规则.然后,分别利用单李雅谱诺夫泛函和多李雅谱诺夫泛函方法,讨论不同情形下的中立型切换控制系统的稳定性,并设计控制器.其次,利用驻留时间方法讨论包含稳定和不稳定子系统的切换中立型系统,设计使得系统指数稳定的依赖于时间的切换规则.
研究不确定性切换中立型控制系统的有界输入有界输出稳定性.其中的不确定性结构为分式不确定性结构,它包括范数有界不确定性.首先结合中立型系统和切换系统的内在性质,得到一般线性切换中立型系统的常数变易公式.然后,结合得到的常数变易公式和自由矩阵的思想,利用驻留时间的方法,得到以线性矩阵不等式表示的稳定性条件.最后,数值仿真验证所得结果的优越性.
对全文进行总结,并指出今后的研究方向.
Addressed in this dissertation is the key dynamics of neutral systems and switchedneutral systems. Several relevant problems attracting more and more attention in this fieldare discussed in detail, and a series of well-established, systematical, and important re-sults is obtained.
The backgrounds and research status of neutral systems and switched neutral sys-tems are introduced. It also provides the readers with some preliminaries and importantdefinitions and lemmas that are frequently used in the remaining chapters.
The robust stability for uncertain linear neutral systems with discrete and distributeddelays(the single time delay and multiple time delay are included) is studied. The uncer-tainties under consideration are norm bounded, and possibly time varying. Some noveldelay-dependent stability criteria are derived and formulated in the form of linear matrixinequalities (LMIs) by a new class of Lyapunov-Krasovskii functionals which is con-structed based on the descriptor model of the system and the method of decomposition.The new criteria are less conservative than the existing ones. The examples are suppliedto illustrate the effectiveness of the results presented in this chapter.
The asymptotical stability of neutral systems with nonlinear perturbations is studied.Some novel delay-dependent asymptotical stability criteria are formulated in terms of lin-ear matrix inequalities (LMIs). The resulting delay-dependent stability criteria are lessconservative than the previous ones owing to the introduction of free-weighting matricesand the Schur’s lemma, based on a class of novel augment Lyapunov functionals.
The delay-dependent bound input bound output(BIBO) stabilization of neutral sys-tems with multiple delays is investigated. Using the method of the descriptor modeltransformation, introducing the free-weighting matrices in the new class of Lyapunov-Krasoviskii functionals, and combining with the matrix analysis technique, the controllerwhich make the systems (BIBO) stable is designed.
The stability analysis for the switched neutral systems is considered. First, wepresent new classes of piecewise Lyapunov functionals and multiple Lyapunov function-als, based on which, two new switching rules are introduced to stabilize the neutral sys-tems. One switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. The other is based on the determination of average dwell timecomputed from a new class of linear matrix inequalities (LMIs). The state-dependentswitching rule is less conservative than the existing results. Similarly, we also analyze thestability of switched neutral systems with nonlinear perturbations. Second, in differentcase, using singular Lyapunov functional and multiple Lyapunov functional respectively,the stabilization for linear uncertain neutral systems with delay in switched control in-put is investigated, and the controller is designed. Third, Based on multiple Lyapunovfunctional approach and dwell-time technique, the stability of the switched neutral sys-tems which both contain the stable subsystems and unstable subsystems is considered.The switching rule which make the switched systems exponential stable is designed. It isshown that by suitably controlling the switching between the stable and unstable modes,the robust stabilization of the switched uncertain neutral systems can be achieved.
The problem of delay-dependent bounded input bounded output (BIBO) stability fora class of switched uncertain neutral systems is studied. The uncertainty is assumed tobe of structured linear fractional from which includes the norm bounded uncertainty as aspecial case. First, by introducing the general variation-of-constants formula of neutralsystems with perturbation, the BIBO stability property of general linear switched neutralsystems with perturbation is established. Next, based on the dwell time approach, andcombined with the introduced free-weighting matrices, the BIBO stability criteria are ob-tained in terms of linear matrix inequalities(LMIs). Finally, the simulation examples aregiven to demonstrate the effectiveness and the potential of the proposed techniques in thischapter.
We summarize the main results obtained in this dissertation, and point out the futureworks that have been the author’s concerns.
介绍中立型系统及切换中立型系统的研究背景和研究现状,提供论文中常用的基本概念,基础知识和重要引理.它们是后续章节讨论的前提.
研究含有分布时滞的中立型系统(包括单分布的中立型系统和多分布时滞的中立型系统两种情形)的渐近稳定性.通过构造新的李雅谱诺夫泛函,结合矩阵分解的技巧和自由矩阵的思想方法,得到保守性较低的时滞相关的稳定性结果.数值实例验证所得结果的有效性和优越性.
研究含有非线性扰动的中立型时滞系统的渐近稳定性问题.通过构造新的扩展李雅谱诺夫泛函,结合自由矩阵的思想,并合理利用Schur补引理,得到保守性较低的时滞依赖的稳定性结论.
研究含有多时滞的中立型系统的有界输入有界输出稳定性问题.利用等价描述系统的方法,在构造李雅谱诺夫泛函过程中适当引入自由矩阵,结合矩阵分析技巧设计使得系统有界输入有界输出稳定的控制器.
讨论切换中立型系统的稳定性分析.首先,提供构造新的分段李雅普诺夫泛函,设计两种使得切换中立型系统稳定的切换规则.其中,依赖于状态的切换规则是通过求解李雅普诺夫-梅兹勒矩阵不等式而设计的,而依赖于时间的切换规则是利用平均驻留时间的方法,并结合线性矩阵不等式求解而得到的.依赖于状态的切换规则降低了现有文献设计的切换规则所带来的保守性.类似地,设计使得切换中立型扰动系统渐近稳定的切换规则.然后,分别利用单李雅谱诺夫泛函和多李雅谱诺夫泛函方法,讨论不同情形下的中立型切换控制系统的稳定性,并设计控制器.其次,利用驻留时间方法讨论包含稳定和不稳定子系统的切换中立型系统,设计使得系统指数稳定的依赖于时间的切换规则.
研究不确定性切换中立型控制系统的有界输入有界输出稳定性.其中的不确定性结构为分式不确定性结构,它包括范数有界不确定性.首先结合中立型系统和切换系统的内在性质,得到一般线性切换中立型系统的常数变易公式.然后,结合得到的常数变易公式和自由矩阵的思想,利用驻留时间的方法,得到以线性矩阵不等式表示的稳定性条件.最后,数值仿真验证所得结果的优越性.
对全文进行总结,并指出今后的研究方向.
Addressed in this dissertation is the key dynamics of neutral systems and switchedneutral systems. Several relevant problems attracting more and more attention in this fieldare discussed in detail, and a series of well-established, systematical, and important re-sults is obtained.
The backgrounds and research status of neutral systems and switched neutral sys-tems are introduced. It also provides the readers with some preliminaries and importantdefinitions and lemmas that are frequently used in the remaining chapters.
The robust stability for uncertain linear neutral systems with discrete and distributeddelays(the single time delay and multiple time delay are included) is studied. The uncer-tainties under consideration are norm bounded, and possibly time varying. Some noveldelay-dependent stability criteria are derived and formulated in the form of linear matrixinequalities (LMIs) by a new class of Lyapunov-Krasovskii functionals which is con-structed based on the descriptor model of the system and the method of decomposition.The new criteria are less conservative than the existing ones. The examples are suppliedto illustrate the effectiveness of the results presented in this chapter.
The asymptotical stability of neutral systems with nonlinear perturbations is studied.Some novel delay-dependent asymptotical stability criteria are formulated in terms of lin-ear matrix inequalities (LMIs). The resulting delay-dependent stability criteria are lessconservative than the previous ones owing to the introduction of free-weighting matricesand the Schur’s lemma, based on a class of novel augment Lyapunov functionals.
The delay-dependent bound input bound output(BIBO) stabilization of neutral sys-tems with multiple delays is investigated. Using the method of the descriptor modeltransformation, introducing the free-weighting matrices in the new class of Lyapunov-Krasoviskii functionals, and combining with the matrix analysis technique, the controllerwhich make the systems (BIBO) stable is designed.
The stability analysis for the switched neutral systems is considered. First, wepresent new classes of piecewise Lyapunov functionals and multiple Lyapunov function-als, based on which, two new switching rules are introduced to stabilize the neutral sys-tems. One switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. The other is based on the determination of average dwell timecomputed from a new class of linear matrix inequalities (LMIs). The state-dependentswitching rule is less conservative than the existing results. Similarly, we also analyze thestability of switched neutral systems with nonlinear perturbations. Second, in differentcase, using singular Lyapunov functional and multiple Lyapunov functional respectively,the stabilization for linear uncertain neutral systems with delay in switched control in-put is investigated, and the controller is designed. Third, Based on multiple Lyapunovfunctional approach and dwell-time technique, the stability of the switched neutral sys-tems which both contain the stable subsystems and unstable subsystems is considered.The switching rule which make the switched systems exponential stable is designed. It isshown that by suitably controlling the switching between the stable and unstable modes,the robust stabilization of the switched uncertain neutral systems can be achieved.
The problem of delay-dependent bounded input bounded output (BIBO) stability fora class of switched uncertain neutral systems is studied. The uncertainty is assumed tobe of structured linear fractional from which includes the norm bounded uncertainty as aspecial case. First, by introducing the general variation-of-constants formula of neutralsystems with perturbation, the BIBO stability property of general linear switched neutralsystems with perturbation is established. Next, based on the dwell time approach, andcombined with the introduced free-weighting matrices, the BIBO stability criteria are ob-tained in terms of linear matrix inequalities(LMIs). Finally, the simulation examples aregiven to demonstrate the effectiveness and the potential of the proposed techniques in thischapter.
We summarize the main results obtained in this dissertation, and point out the futureworks that have been the author’s concerns.
引文
[1] A.A. Agrachev, D. Liberzon. Lie-algebric stability criteria for switched systems, SIAMJournal on Control and Optimization, 2001, 40:253-269.
[2] R.P. Agarwal, S.R. Grace. Asymptotic stability of differential systems of neutral type. Ap-plied Mathematics Letters,2000,13:15-19.
[3] M. Akar, A.Paul, M.G. Safonov, U. Mitra. Conditions on the stability of a class of second-order switched systems. IEEE Transaction on Automatic Control, 2006, 51:338-340.
[4] A. Alessandri, M. Sanguineti. Connections between Lp stability and asymptotic stability ofnonlinear switched systems. Nonlinear Analysis: Hybrid Systems, 2007, 1:501-509.
[5] M.S. Alwan, X.-Z. Liu. On stability of linear and weakly nonlinear switched systems withtime delay. Mathematical and Computer Modelling, 2008, 48:1150-1157.
[6] M.S. Alwan, X.-Z. Liu, B. Ingalls. Exponential stability of singularly perturbed switchedsystems with time delay. Nonlinear Analysis: Hybrid Systems, 2008, 2:913-921.
[7] P.J. Antsaklis. Special issue on hybrid systems: Theory and applications-A brief introduc-tion to the theory and applications of hybrid systems. Proceedings of IEEE, 2000, 88:887-897.
[8] L. Bakule. Stabilization of uncertain switched symmetric composite systems. NonlinearAnalysis: Hybrid Systems, 2007,1:188-197.
[9] J.-D. Bao, F.-Q. Deng, Q. Luo. Robust Stability on Nonlinear Neutral Systems with Uncer-tain Time- delay.华南理工大学学报(自然科学版), 2003, 3:21-25.
[10] G.A. Batholomeus, M. Dambrine, J.P. Richard. Stability of perturbed systems with time-varying delays. Systems Control Letters, 1997, 31:155-163.
[11] P.A. Bliman. Lyapunov Equation for the stability of linear delay systems of Retarded andNeutral Type. IEEE Transactions on Automatic Control, 2002, 47:327-335.
[12] C. Bonneta, J.R. Partington. Analysis of fractional delay Systems of retarded and neutraltype. Automatica, 2002,38:1133-1138.
[13] S. Boyd, E. Ghaoui, E. Feron, V. Balakrishnan. Linear matrix inequalities in system andcontrol theory, Philadelphia: SIAM, 1994.
[14] D.-Q. Cao, P. He. Stability criteria of linear neutral systems with a single delay. AppliedMathematics and Computation, 2004, 148:135-143.
[15] Y.-Y. Cao, J. Lam, Computation of robust stability bounds for time-delay systems with non-linear time-varying perturbation. International Journal of Systems Science, 2000, 31:359-365.
[16] D. Chatterjee, D. Liberzon. On stability of randomly switched nonlinear systems. IEEETrans. on Automatic Control, 2007, 52:2390-2394.
[17] J.-D. Chen. Robust control for uncertain neutral systems with time-delays in state and con-trol input via LMI and Gas. Applied Mathematics and Computation, 2004, 157:535-548.
[18] J.-D. Chen. New stability criteria for a class of neutral systems with discrete and distributedtime-delays: an LMI approach. Applied Mathematics and Computation, 2004, 150:719-736
[19] J.-D. Chen, C.-H. Lien, K.-K.Fan, et al. Criteria for asymptotic stability of a class of neutralsystems via a LMI approach. IEE Pro.Control Theory Appl., 2001, 148:442-447.
[20] W.-H. Chen, Z.-H. Guan, X.-M. Lu. Robust H∞control of neutral delay systems withMarkovian jumping parameter. Control Theory & Applications, 2003, 20:776-778.
[21] W.-H. Chen, W.-X. Zheng. Delay-dependent robust stabilization for uncertain neutral sys-tems with distributed delays. Automatica, 2007, 43:95-104.
[22]丛玉豪,杨彪.广义中立型系统的渐近稳定性.纯粹数学与应用数学,2000, 3:31-36.
[23] M.A. Cruz, J.K. Hale. Stability of functional differential equations of neutral type. Journalof differential equations, 1970, 7: 334-355.
[24] J. Daafouz, R. Riedinger, C. Iung. Stability analysis and control synthesis for switched sys-tems: a switched Lyapunov function approach. IEEE Transactions on Automatic Control,2002, 47:1883-1887.
[25] DanIv’anescu, S.L. Niculescu. On delay-dependent stability for linear neutral systems.Automatica, 2003, 39:255-261.
[26] R.A. Decarlo, M.S. Branicky, S. Pettersson, B. Lennartson. Perspectives and results on thestability and stabilizability of hybrid systems. Proceedings of the IEEE: Special issue onhybrid systems, 2000:1069–1082.
[27] R. DeCarlo, M.S. Branicky, S. Pettersson, B. Lennartson. Perspectives and results on thestability and stabilizability of hybrid systems. Proceedings of IEEE, 2000, 88:1069-1082.
[28] D.-S. Du, B. Jiang, P. Shi, S. Zhou. H∞filtering of discrete-time switched systems withstate delays via switched Lyapunov function approach, IEEE Trans. on Automatic Control,2007, 52:1520-1525.
[29] D.-S. Du, B. Jiang, P. Shi, S.-S. Zhou. Robust l2-l∞control for uncertain discrete-timeswitched systems with delays. Circuits, Systems & Signal Processing, 2006, 25:729-744.
[30] S. Engell, S. Kowalewski, C. Schulz, O. Strusberg. Continuous-discrete interactions inchemical processing plants. Proceedings of IEEE, 2000, 88:1050-1068.
[31] K.-K. Fan, J.-D. Chen. Delay-dependent stability criterion for neutral time-delay systemsvia linear matrix inequality approach. Journal of Mathematical Analysis and Applications,2002, 237:580-589.
[32] K.-K. Fan, C.-H. Lien, J.G. Hsieh. Asymptotic Stability for a Class of Neutral Systemswith Discrete and Distributed Time Delays. Journal of optimization theory and applications,2002, 114:705-716.
[33] L. Fang, H. Lin, P.J. Antsaklis. Stabilization and performance analysis for a class ofswitched systems. Proceedings of 43rd IEEE Conf. Decision Control, 2004:3265-3270.
[34] E. Fridman. New Lyapunov-Krasovskii functionals for stability of linear retarded and neu-tral type systems. Systems & Control letters, 2001,43:309-319.
[35] E. Fridman, U.A. Shaked. A descriptor system approach to H∞control of linear time-delaysystems. IEEE Transaction on AutomaticControl, 2002, 47:253-270.
[36] Y.-L. Fu, X.-X.Liao. BIBO stabilization of stochastic delay systems with uncertainty. IEEETransactions on Automatic Control, 2003, 48:133-138.
[37] L. Gao, Y. Wu. A design scheme of variable structure H∞control for uncertain singularmarkov switched systems based on linear matrix inequality method. Nonlinear Analysis:Hybrid Systems, 2007, 1:306-316.
[38] K.M. Garg. Theory of Differentiation: A Unified Theory of differentiation via new derivatetheorems and new derivatives, Wiley-Interscience, New York, 1998.
[39] J.C. Geromel, P. Colaneri. Stability and stabilization of continuous-time switched linearsystems. SIAM Journal on Control and Optimization, 2006, 45:1915-1930.
[40] K.-Q. Gu. An integral inequality in the stability problem of time-delay systems. Proceedingsof 39th IEEE CDC, Sydney, Australia, 2000:2805-2810.
[41] K.-Q. Gu, S.I. Niculescu. Further remarks on additional dynamics in various model trans-formations of linear delay systems. IEEE Transactions on Automatic Control, 2001, 46:497-500.
[42] K.-Q. Gu, V.L. Kharitonov, J. Chen. Stability of time-delay systems, Birkhauser, Basel,2003.
[43] Z.-H. Guan, H. Zhang. Stabilization of complex network with hybrid impulsive and switch-ing control. Chaos Solitons & Fractals, 2008, 37:1372-1382.
[44] J.K. Hale. Theory of functional differential equations. Springer-Verlag, 1977.
[45] J.K. Hale, P.M. Amorez. Stability in neutral equations. Nonlinear Analysis, 1977, 1: 161-173.
[46] J.K. Hale, S.M. VerduynLunel. Introduction to functional differential equations. New York:Springer-Verlag, 1993.
[47] Q.-L. Han. A descriptor system approach to robust stability of uncertain neutral systemswith discrete and distributed delays. Automatica, 2004, 40:1791-1796.
[48] Q.-L. Han. On stability of linear neutral systems with mixed time delays: A discretizedLyapunov functional approach. Automatica, 2005, 47:1209-1218.
[49] Q.-L. Han. Robust stability of uncertain delay-differential systems of neutral type. Auto-matica, 2002, 38:719-723.
[50] Q.-L. Han. Robust stability for a class of linear systems with time-varying delay and non-linear perturbations. Computer and Mathematics with Applications, 2004, 47:1201-1209.
[51] Q.-L. Han. Stability of linear neutral systems with linear fractional norm-bounded uncer-tainty. American Control Conference, 2005:2827-2832.
[52] Q.-L. Han, K.-Q. Gu. On Robust Stability of Time-Delay Systems With Norm -BoundedUncertainty. IEEE transactions on automatic control, 2001, 46:1426-1432.
[53] Q.-L. Han, L. Yu. Robust stability of linear neutral systems with nonlinear parameter per-turbations, IEE Proceedings Control Theory & Applications, 2004, 151:539-546.
[54] Q.-L. Han, X.-H. Yu, K.-Q. Gu. On Computing the Maximum Time-Delay Bound for Sta-bility of Linear Neutral Systems. IEEE transactions on automatic control, 2004, 49:2281-2287.
[55] P. He, D.-Q. Cao. Algebraic stability criteria of linear neutral systems with multiple timedelays. Applied Mathematics and Computation, 2004,155:643-653.
[56] Y. He, M. Wu. On Delay- dependent Stability of Neutral Systems With Nonlinear Pertur-bations. Mathematical theory and applications, 2003, 3:91-96.
[57] Y. He, Q.-G. Wang, L. Xie, C. Lin. Further improvement of free-weighting matrices tech-nique for systems with time-varying delay. IEEE Transaction on Automatic Control, 2007,52:293-299.
[58] Y. He, Q.-G. Wang, C. Lin, M. Wu. Augmented Lyapunov functional and delay dependentstability criteria for neutral systems. International Journal of Robust Nonlinear Control.2005, 15:923-933.
[59] Y. He, M. Wu, J.-H. She. Delay-dependent robust stability criteria for uncertain neutralsystems with mixed delays. Systems & Control Letters, 2004, 51:57 -65.
[60] J.P. Hespanha. Stabilization through hybrid control. Encyclopedia of Life Support Systems(EOLSS),Control Systems, Robotics, and Automation. Oxford, UK, 2004.
[61] J.P. Hespanha. Uniform stability of switched linear systems: Extensions of Lasalle’s invari-ance principle. IEEE Transactions on Automatic Control, 2004, 49:470-482.
[62] J.P. Hespanha, A.S. Morse. Stability of switched systems with average dwell-time. In Proc.38th IEEE Conference Decision Control, 1999:2655-2660.
[63] R. Horowitz, P. Varaiya. Control design of an automated highway system. Proceedings ofIEEE, 2000, 88:913-925.
[64] G.-D. Hu, G.-D. Hu, B. Cahlon. Algebraic criteria for stability of linear neutral systemswith a single delay. Journal of Computational and Applied Mathematics, 2001, 135:125-133.
[65] G.-D. Hu, G.-D. Hu. Some simple stability criteria of neutral delay-differential systems.Applied Mathematics and Computation, 1996, 80:257-271.
[66] K. Ito, T.J. Tarn. A linear quadratic optimal control for neutral systems. Nonlinear Analysis,1985, 9:699-727.
[67] H.R. Karimi, M. Zapateiro, N.S. Luo. Stability analysis and control synthesis of neutralsystems with time-varying delays and nonlinear uncertainties. Chaos, Solitons & Fractals,2009, 42:595-603.
[68] D.Y. Khusainow, E.A. Yunkova. Investigation of the stability of linear-systems of neutraltype by the Lyapunov function menthod. Differential Equations, 1988, 24:424-431.
[69] S. Kim, S.A. Campbell, X.-Z. Liu. Stability of a class of linear switching systems with timedelay. IEEE Trans. on Circuits and Systems-I: Regular Papers, 2006, 53:384-393.
[70] V.B. Kolmanovskii, J.P. Richard. Stability of some linear systems with delays. IEEE Trans-actions on Automatic Control, 1999, 44:984-989.
[71] J. Lam, H. Gao, C. Wang. Stability analysis for continuous systems with two additive time-varying delay components. Systems & Control Letters, 2007, 56: 16-24.
[72]李宏飞,罗学波.具有非线性扰动的中立型系统的鲁棒稳定性.西南师范大学学报(自然科学版), 2004, 4:539-545.
[73]廖晓昕.稳定性的理论、方法和应用.武汉:华中科技大学出版社, 2002, 42-65.
[74] L.S. Lasdon. Optimization Theory for Large Scale Systems, Series of Operation Research,MacMillan, New York, 1970.
[75] H. Li, H.-B. Li, S.-M. Zhong. Some new simple stability criteria of linear neutral systemswith a single delay. Journal of Computational and Applied Mathematics, 2007, 200:441-447.
[76] H. Li, H.-B. Li, S.-M. Zhong. Stability of neutral type descriptor system with mixed delays.Chaos,solitions & Fractals, 2007, 5:1796-1800.
[77] P. Li, S.-M. Zhong. BIBO stabilization for system with multiple mixed delays and nonlinearperturbations, Applied Mathematics and Computation, 2008, 196:207-213.
[78] P. Li, S.-M. Zhong. BIBO stabilization of time-delayed systemwith nonlinear perturbation.Applied Mathematics and Computation, 2008, 195:264-269.
[79] P. Li, S-M. Zhong. BIBO stabilization of piecewise switched linear systems with delaysand nonlinear perturbations. Applied Mathematics and Computation, 2009, 213:405-410.
[80] P. Li, S-M. Zhong, J.-Z. Cui. Stability analysis of linear switching systems with time delays.Chaos, Solitons & Fractals, 2009, 40:474-480.
[81] R.-H. Li, Y.-M. Hou. Convergence and stability of numerical solutions to SDDEs withMarkovian switching. Applied Mathematics and Computation, 2006, 175:1080-1091.
[82]李顺洋,田彦涛. Markov切换系统的随机稳定性分析.控制工程, 2004, 11:325-327
[83] D. Liberzon. Switching in Systems and Control. Birkhauser, Boston, 2003.
[84] D. Liberzon, J.P. Hespanha, A.S. Morse. Stability of switched linear systems: A Lie-algebraic condition. System & Control Letter, 1999, 37:117-122.
[85] D. Liberzon, A.S. Morse. Basic problems in stability and design of switched systems. IEEEControl Systems Magazine, 1999, 19:59-70.
[86] D. Liberzon, R. Tempo. Common Lyapunov functions and gradient algorithms. IEEETransactions on Automatic Control, 2004, 49:990-994.
[87] C.-H. Lien. Asymptotic criterion for neutral systems with multiple time-delays. ElectronicsLetters, 1999,35:850-852.
[88] C.-H. Lien, K.-W Yu, J.G. Hsieh. Stability conditions for a class of neutral systems withmultiple time delays. Journal of Mathematical Analysis and Applications, 2000, 245:20-27.
[89] H. Lin, P.J. Antsaklis. Stability and stabilizability of switched linear systems: a short sur-veyof recent results. Proceedings of the 2005 IEEE International Symposium on IntelligentControl, 2005:24-29.
[90] H. Lin, P.J. Antsaklis. Stability and Stabilizability of Switched Linear Systems: A Surveyof Recent Results. IEEE Transactions on Automatic Control, 2009, 54:308-322.
[91] D.-Y. Liu, X.-Z. Liu, S.-M. Zhong. Delay-dependent robust stability and control synthe-sis for uncertain switched neutral systems with mixed delays. Applied Mathematics andComputation, 2008, 202:828-839.
[92] D.-Y. Liu, S.-M. Zhong, L.-L. Xiong. On robust stability of uncertain neutral systems withmultiple delays. Chaos, Solitons & Fractals, 2009, 39:2332-2339.
[93] X.-G. Liu, M. Wu, R. Martin. Delay-dependent stability analysis for uncertain neutral sys-tems with time-varying delays. Mathematics and Computers in Simulation, 2007, 75:15-27.
[94] X.-G. Liu, M. Wu, R. Martin, M.-L. Tang. Stability analysis for neutral systems with mixeddelays. Journal of Computational and Applied Mathematics, 2007, 202:478-497.
[95] X.-Z. Liu, K.L. Teo, H.-T. Zhang, G.-R. Chen. Switching control of linear systems forgenerating chaos. Chaos Solitons & Fractals, 2006, 30:725–733.
[96] Y. Liu, F. Wang. Razumikhin-Lyapunov functional method for the stability of impulsiveswitched systems with time delay. Mathematical and Computer Modelling, 2009, 49:249-264.
[97] C. Livadas, J. Lygeros, N.A. Lynch. High-level modeling and analysis of the traffic alertand collision avoidance system. Proceedings of IEEE, 2000, 88:926-948.
[98] J.L. Mancilla-Aguilar, R.A. Garc′?a. A converse Lyapunov theorem for nonlinear switchedsystems. Systems & Control Letters, 2000, 41:67-71.
[99] M. Margaliot. A counterexample to a conjecture of gurvits on switched systems. IEEETransaction on Automatic Control, 2007, 52:1123-1126.
[100] O. Mason, R. Shorten. The geometry of convex cones associated with the Lyapunov in-equality and the common Lyapunov function problem. Electronic Journal of Linear Alge-bra, 2005, 12:42-63.
[101] G. Michaletzky, L. Gerencser. BIBO stability of linear switching systems. IEEE Transac-tions on Automatic Control, 2002, 47:1895-1898.
[102] A.N. Michel. Recent trends in the stability analysis of hybrid dynamical systems. IEEETransactions on Circuits System(I), 1999, 46:120-134.
[103] Y.-S. Moon. Robust control of time-delay system using linear matrix inequalities. Ph.D.Thesis, Seoul National University, 1998.
[104] K.S. Narendra, J. Balakrishnan. A common Lyapunov function for stable LTI systems withcommuting A-matrices. IEEE Transactions on Automatic Control, 1994, 39:2469-2471.
[105] B. Ni, Q.-L. Han. On stability for a Class of Neutral Delay-Differential systems.Pro.American Control Conference, Arington, 2001:4544-4549.
[106]倪涛洋,黎培兴,李彩霞.中立型线性微分方程的稳定性. 2005, 1:144-147.
[107] S.L. Niculescu. Optimizing model transformations in delay-dependent analysis of neutralsystems. Nonlinear Analysis, 2001, 47:5379-5390.
[108] S.L. Niculescu. Further remarks on delay-dependent stability of linear neutral systems. Pro-ceeding of MTNS, 2000:4368-4372.
[109] S.L. Niculescu. On Delay-dependent stability in Neutral systems. Proceeding of AmericanControl Conference, Arlington, 2001:3384-3388.
[110] C.-H. Lien, K.-W. Yu, J.G. Hsieh. Stability conditions for a class of neutral systems withmultiple time delays. Journal of Mathematical Analysis and Application, 2000, 245:20-27.
[111] A. Papachristodoulou, S. Prajna. A tutorial on sum of squares techniques for systems anal-ysis. In Proceeding of 2005 American Control Conference, 2005.
[112] J.H. Park. A new delay-dependent criterion for neutral systems with multiple delays. Jour-nal of Computational and Applied Mathematics, 2001,136:177-184.
[113] J.H. Park. Novel robust stability criterion for a class of neutral systems with mixed delaysand nonlinear perturbations. Applied Mathematics and Computation, 2005, 161:413-421.
[114] J.H. Park. Robust guaranteed cost control for uncertain linear differential systems of neutraltype. Applied Mathematics and Computation, 2003, 140:523-535.
[115] J.H. Park. Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments. Mathematics and Computers in Simulation, 2002, 59:401-412.
[116] J.H. Park, H.Y. Jung. On the exponential stability of a class of nonlinear systems includingdelayed perturbations. Journal of Computational and Applied Mathematics, 2003, 159:467-471.
[117] J.H. Park, O. Kwon. On new stability criterion for delay-differential systems of neutral type.Applied Mathematics and Computation, 2005, 162:627-637.
[118] J.H. Park, O. Kwon. On guaranteed cost control of neutral systems by retarded integral statefeedback. Applied Mathematics and Computation, 2005,165:393-404.
[119] J.H. Park, S.Won. Stability analysis for neutral delay-differential systems. Journal of theFranklin Institute, 2000,337:1-9.
[120] J.H. Park, S. Won. Asymptotic Stability of Neutral Systems with Multiple Delays. Journalof optimization theory and applications, 1999, 103:183-200.
[121] P. Park. A delay-dependent stability criterion for systems with uncertain time-invariant de-lays. IEEE Transactions on Automatic Control, 1999,44:876-877.
[122] J.R. Partington, C. Bonnet. H∞and BIBO stabilization of delay systems of neutral type.Systems & Control Letters, 2004, 52:283-288.
[123] S. Pettersson, B. Lennartson. Hybrid system stability and robustnessverification using linearmatrix inequalities. International journal of Control, 2002, 75:1335-1355.
[124] D. Pepyne, C. Cassandaras. Optimal control of hybrid systems in manufacturing. Proceed-ings of IEEE, 2000, 88:1008-1122.
[125] S. Prajna, A. Papachristodoulou. Analysis of switched and hybrid systems beyond piece-wise quadratic methods. Proceeding of 42nd IEEE Conference of Decision Control,2003:2779-2784.
[126] M.D. Sen, J.L. Malaina, A. Gallego, J.C. Soto. Stability of non-neutral and neutral dynamicswitched systems subject to internal delays. American Journal of Applied Sciences, 2005,2:1481-1490.
[127] M. Slemrod, E.F. Infante, Asymptotic stability criteria for linear systems of differentialequations of neutral type and their discrete analogues. Journal of Mathematical Analysisand Application, 1972, 38:399-415.
[128] M. Song, T. Tran, N. Xi, Integration of task scheduling, action planning, and control inrobotic manufacturing systems. Proceedings of IEEE, 2000, 88:1097-1107.
[129] M.-H. Sun, James Lam, S.-Y. Xu, Y. Zou. Robust exponential stabilization for Markovianjump systems with mode-dependent input delay. Automatica, 2007, 43:1799-1807.
[130] X.-M. Sun, J. Fu, H.-F. Sun, J. Zhao, Stability of linear switched neutral delay systems.Proceedings of The Chinese Society for Electrical Engineering, 2005, 25:42-46.
[131] X.-M. Sun, J. Zhao, D.J. Hill, Stability and L2-gain analysis for switched delay systems: Adelay-dependent method. Automatica, 2006, 42:1769-1774.
[132] Y.-G. Sun, L. Wang, G. Xie. Stability of switched systems with time-varying delays: de-laydependentcommon Lyapunov functional approach. Proceedings of the 2006 AmericanControl Conference, 2006:1544-1549.
[133] Z.-D. Sun, Stabilizability and Insensitivity of Switched Linear Systems. IEEE Transactionson Automatic Control, 2004, 49:1133-1137.
[134] Z.-D. Sun, S.S. Ge, Analysis and synthesis of switched linear control systems. Automatica,2005, 41:181-195.
[135] Z.-D. Sun, S.S. Ge, Switched Linear Systems: Control and Design. London: Springer-Verlag, 2005.
[136] J.-K. Tian, L.-L. Xiong, J.-X. Liu, X.-J. Xie, Novel delay-dependent robust stability criteriafor uncertain neutral systems with time-varying delay. Chaos, Solitons & Fractals, 2009,40:1858-1866.
[137] M.G. Todorov, M.D. Fragoso, Output feedback h∞control of continuous-time infinitemarkovian jump linear systems via LMI methods. SIAM Journal Control optimal, 2008,47:950-974.
[138] F.-H. Tu, X.-F. Liao, W. Zhang. Delay-dependent asymptotic stability of a two-neuron sys-tem with different time delays, Chaos, Solitons & Fractals, 2006, 2: 437-447.
[139] H.-L. Xu, X.-Z. Liu, K.L. Teo. A LMI approach to stability analysis and synthesis of im-pulsive switched systems with time delays. Nonlinear Analysis: Hybrid Systems, 2008,2:38-50.
[140] P. Varaiya, Smart cars on smart roads: Problems of control. IEEE Transactions on Auto-matic Control, 1993, 38:195-207.
[141] M. Vidyasagar, Nonlinear systems analysis(2nd ed). Upper Saddle River, NJ, USA:Prentice-Hall, Inc., 1992.
[142] R. Wang, M. Liu, J. Zhao. Reliable H∞control for a class of switched nonlinear systemswith actuator failures. Nonlinear Analysis: Hybrid Systems, 2007, 1:317-325.
[143] H. Wu, K. Mizukami. Robust stabilization of uncertain linear dynamical systems. Interna-tional Journal of Systems Science, 1993, 24:265-276.
[144] G.-M. Xie, L. Wang, Controllability and stabilizability of switched linear-systems. Systems& Control Letters, 2003, 48:135-155.
[145] G.-M. Xie, L. Wang. Reachability realization and stabilizability of switched linear discrete-time systems. Journal of Mathematical Analysis and Applications, 2003, 280:209-220.
[146] L. Xie. Output feedback H∞control of systems with parameter uncertainty. InternationalJournal Control, 1996, 63:741-750.
[147] J.-L. Xiong, James Lam, H.-J. Gao, DanielW.C. Ho. On robust stabilization of Markovianjump systems with uncertain switching probabilities. Automatica, 2005, 41:897-903.
[148] L.-L. Xiong, S.-M. Zhong, J.-K. Tian. Novel robust stability criteria of uncertain neutralsystems with discreteand distributed delays. Chaos, Solitons & Fractals, 2009, 40:771-777.
[149] W.-J. Xiong , J.-L. Liang. Novel stability criteria for neutral systems with multiple timedelays. Chaos,solitions & Fractals, 2007, 5:1735-1741.
[150] D.-Y. Xu, S.-M. Zhong. Robust BIBO stabilization of linear large-scale systems with non-linear delay perturbations, Dynamics of Continuous, Discrete and Impulsive Systems, 1996,2:511-520.
[151] D.-Y. Xu, S.-M. Zhong, M. Li. BIBO stabilization of large-scale systems, Control Theoryand Applications, 1995, 12:758-763.
[152] V.A. Yakubovich, S-procedure in nonlinear control theory. Vestnik. Leningradskogo Uni-versiteta, Ser. Matematika, Series1, 62-77.
[153] J. Yang, S.-M. Zhong, L.-L. Xiong, A descriptor system approach to non-fragile H∞con-trol for uncertain fuzzy neutral systems, Fuzzy Sets and Systems, 2009, 160:423-438.
[154] B. Yang, T. Li, Y.- H. Jiang. On the stability of neutral systems with multiple delays. Amer-ican control conference, 2003:5066-5067.
[155] B. Yang, R.J. Zhu, T. Li. Delay-dependent stability criterion for a class of neutral time delaysystems. Proceedings of the American Control Conference, 2003:2694-2697.
[156] H. Ye, A.N. Michel, K.-N. Wang. Robust stability of Linear Time-Delay systems: Retardedand Neutral Types. IEEE Transactions on Automatic Control,1995,40:1488-1491.
[157] D. Yue, S. Won, O. Kwon. Delay dependent stability of neutral systems with time delay: anLMI approach. IEE Proceedings, 2003, 150:23-27.
[158] G.-S. Zhai, B. Hu, K. Yasuda, A.N. Michel. Disturbance attenuation properties of time-controlled switched systems. Journal of Franklin Institute, 2001, 338:765–779.
[159] G.-S. Zhai, B. Hu, K. Yasuda, A.N. Michel. Qualitative analysis of discrete-time switchedsystems. Proceedings of 2002 American Control Conference, 2002:1880-1885.
[160] G.-S. Zhai, H. Lin. Controller failure time analysis for symmetric H1 control systems. In-ternational journal of control, 2004, 77:598-605.
[161] G.-S. Zhai, X.-P. Xu, H. Lin, A.N. Michel. Analysis and design of switched normal systems.Nonlinear Analysis: Theory, Methods & Applications, 2006, 65:2248-2259.
[162] K.-Y. Zhang, D.-Q. Cao. Further results on asymptotic stability of linear neutral systemswith multiple delays. Journal of the Franklin Institute, 2007, 344:858-866.
[163]张发明.中立型时滞系统的渐近稳定性.湘潭大学自然科学学报, 2002,4:92-96.
[164]张克,跃杨苏.线性中立型时滞系统的稳定性判据.西南交通大学学, 2006, 3:386-381.
[165] W.-A. Zhang, L. Yu, Delay-dependent Robust Stability of Neutral Systems with MixedDelays and Nonlinear Perturbations. Acta Automatica Sinica, 2007, 33:863-866.
[166]张先明,吴敏,何勇.中立型线性时滞系统的时滞相关稳定性.自动化学报, 2004,30:624-628.
[167] Y.-P. Zhang, X.-Z, Liu, H. Zhu, Stability analysis and control synthesis for a class ofswitched neutral systems. Applied Mathematics and Computation, 2007, 190:1258-1266.
[168]张先明,吴敏,何勇.中立型时滞系统得时滞相关稳定性.自动化学报, 2004, 30:624-628.
[169] Y.-P. Zhang, X.-Z. Liu, H. Zhu. Stability analysis and control synthesis for a class ofswitched neutral systems. Applied Mathematics and Computation, 2007, 190:1258-1266.
[170] J. Zhao, J.H. David. On stability, L2-gain and H∞control for switched systems, Automat-ica, 2008, 44:1220-1232.
[171] J. Zhao, G.M. Dimirovski. Quadratic stability of a class of switched nonlinear systems.IEEE Transaction on Automatic Control, 2004, 49:574-578.
[172] Z.-R. Zhao, W. Wang, B. Yang. Delay and its time-derivative dependent robust stability ofneutral control system. Applied Mathematics and Computation, 2007, 187:1326-1332.
[173]曾铭涛,桂卫华,唐朝晖.一类变时滞中立型系统的全局指数稳定性研究.计算机工程与科学, 2005, 27:77-81.
[174] S.-S. Zhou, J. Lam, Robust stabilization of delayed singular systems with linear fractionalparametric uncertainties. Circuits Systems Signal Processing, 2003, 22:579-588.
[175] Z. Zou, Y. Wang. New stability criterion for a class of linear systems with time-varyingdelay and nonlinear perturbations, IEE Proceedings of Control Theory and Applications,2006, 153:623-626.
[2] R.P. Agarwal, S.R. Grace. Asymptotic stability of differential systems of neutral type. Ap-plied Mathematics Letters,2000,13:15-19.
[3] M. Akar, A.Paul, M.G. Safonov, U. Mitra. Conditions on the stability of a class of second-order switched systems. IEEE Transaction on Automatic Control, 2006, 51:338-340.
[4] A. Alessandri, M. Sanguineti. Connections between Lp stability and asymptotic stability ofnonlinear switched systems. Nonlinear Analysis: Hybrid Systems, 2007, 1:501-509.
[5] M.S. Alwan, X.-Z. Liu. On stability of linear and weakly nonlinear switched systems withtime delay. Mathematical and Computer Modelling, 2008, 48:1150-1157.
[6] M.S. Alwan, X.-Z. Liu, B. Ingalls. Exponential stability of singularly perturbed switchedsystems with time delay. Nonlinear Analysis: Hybrid Systems, 2008, 2:913-921.
[7] P.J. Antsaklis. Special issue on hybrid systems: Theory and applications-A brief introduc-tion to the theory and applications of hybrid systems. Proceedings of IEEE, 2000, 88:887-897.
[8] L. Bakule. Stabilization of uncertain switched symmetric composite systems. NonlinearAnalysis: Hybrid Systems, 2007,1:188-197.
[9] J.-D. Bao, F.-Q. Deng, Q. Luo. Robust Stability on Nonlinear Neutral Systems with Uncer-tain Time- delay.华南理工大学学报(自然科学版), 2003, 3:21-25.
[10] G.A. Batholomeus, M. Dambrine, J.P. Richard. Stability of perturbed systems with time-varying delays. Systems Control Letters, 1997, 31:155-163.
[11] P.A. Bliman. Lyapunov Equation for the stability of linear delay systems of Retarded andNeutral Type. IEEE Transactions on Automatic Control, 2002, 47:327-335.
[12] C. Bonneta, J.R. Partington. Analysis of fractional delay Systems of retarded and neutraltype. Automatica, 2002,38:1133-1138.
[13] S. Boyd, E. Ghaoui, E. Feron, V. Balakrishnan. Linear matrix inequalities in system andcontrol theory, Philadelphia: SIAM, 1994.
[14] D.-Q. Cao, P. He. Stability criteria of linear neutral systems with a single delay. AppliedMathematics and Computation, 2004, 148:135-143.
[15] Y.-Y. Cao, J. Lam, Computation of robust stability bounds for time-delay systems with non-linear time-varying perturbation. International Journal of Systems Science, 2000, 31:359-365.
[16] D. Chatterjee, D. Liberzon. On stability of randomly switched nonlinear systems. IEEETrans. on Automatic Control, 2007, 52:2390-2394.
[17] J.-D. Chen. Robust control for uncertain neutral systems with time-delays in state and con-trol input via LMI and Gas. Applied Mathematics and Computation, 2004, 157:535-548.
[18] J.-D. Chen. New stability criteria for a class of neutral systems with discrete and distributedtime-delays: an LMI approach. Applied Mathematics and Computation, 2004, 150:719-736
[19] J.-D. Chen, C.-H. Lien, K.-K.Fan, et al. Criteria for asymptotic stability of a class of neutralsystems via a LMI approach. IEE Pro.Control Theory Appl., 2001, 148:442-447.
[20] W.-H. Chen, Z.-H. Guan, X.-M. Lu. Robust H∞control of neutral delay systems withMarkovian jumping parameter. Control Theory & Applications, 2003, 20:776-778.
[21] W.-H. Chen, W.-X. Zheng. Delay-dependent robust stabilization for uncertain neutral sys-tems with distributed delays. Automatica, 2007, 43:95-104.
[22]丛玉豪,杨彪.广义中立型系统的渐近稳定性.纯粹数学与应用数学,2000, 3:31-36.
[23] M.A. Cruz, J.K. Hale. Stability of functional differential equations of neutral type. Journalof differential equations, 1970, 7: 334-355.
[24] J. Daafouz, R. Riedinger, C. Iung. Stability analysis and control synthesis for switched sys-tems: a switched Lyapunov function approach. IEEE Transactions on Automatic Control,2002, 47:1883-1887.
[25] DanIv’anescu, S.L. Niculescu. On delay-dependent stability for linear neutral systems.Automatica, 2003, 39:255-261.
[26] R.A. Decarlo, M.S. Branicky, S. Pettersson, B. Lennartson. Perspectives and results on thestability and stabilizability of hybrid systems. Proceedings of the IEEE: Special issue onhybrid systems, 2000:1069–1082.
[27] R. DeCarlo, M.S. Branicky, S. Pettersson, B. Lennartson. Perspectives and results on thestability and stabilizability of hybrid systems. Proceedings of IEEE, 2000, 88:1069-1082.
[28] D.-S. Du, B. Jiang, P. Shi, S. Zhou. H∞filtering of discrete-time switched systems withstate delays via switched Lyapunov function approach, IEEE Trans. on Automatic Control,2007, 52:1520-1525.
[29] D.-S. Du, B. Jiang, P. Shi, S.-S. Zhou. Robust l2-l∞control for uncertain discrete-timeswitched systems with delays. Circuits, Systems & Signal Processing, 2006, 25:729-744.
[30] S. Engell, S. Kowalewski, C. Schulz, O. Strusberg. Continuous-discrete interactions inchemical processing plants. Proceedings of IEEE, 2000, 88:1050-1068.
[31] K.-K. Fan, J.-D. Chen. Delay-dependent stability criterion for neutral time-delay systemsvia linear matrix inequality approach. Journal of Mathematical Analysis and Applications,2002, 237:580-589.
[32] K.-K. Fan, C.-H. Lien, J.G. Hsieh. Asymptotic Stability for a Class of Neutral Systemswith Discrete and Distributed Time Delays. Journal of optimization theory and applications,2002, 114:705-716.
[33] L. Fang, H. Lin, P.J. Antsaklis. Stabilization and performance analysis for a class ofswitched systems. Proceedings of 43rd IEEE Conf. Decision Control, 2004:3265-3270.
[34] E. Fridman. New Lyapunov-Krasovskii functionals for stability of linear retarded and neu-tral type systems. Systems & Control letters, 2001,43:309-319.
[35] E. Fridman, U.A. Shaked. A descriptor system approach to H∞control of linear time-delaysystems. IEEE Transaction on AutomaticControl, 2002, 47:253-270.
[36] Y.-L. Fu, X.-X.Liao. BIBO stabilization of stochastic delay systems with uncertainty. IEEETransactions on Automatic Control, 2003, 48:133-138.
[37] L. Gao, Y. Wu. A design scheme of variable structure H∞control for uncertain singularmarkov switched systems based on linear matrix inequality method. Nonlinear Analysis:Hybrid Systems, 2007, 1:306-316.
[38] K.M. Garg. Theory of Differentiation: A Unified Theory of differentiation via new derivatetheorems and new derivatives, Wiley-Interscience, New York, 1998.
[39] J.C. Geromel, P. Colaneri. Stability and stabilization of continuous-time switched linearsystems. SIAM Journal on Control and Optimization, 2006, 45:1915-1930.
[40] K.-Q. Gu. An integral inequality in the stability problem of time-delay systems. Proceedingsof 39th IEEE CDC, Sydney, Australia, 2000:2805-2810.
[41] K.-Q. Gu, S.I. Niculescu. Further remarks on additional dynamics in various model trans-formations of linear delay systems. IEEE Transactions on Automatic Control, 2001, 46:497-500.
[42] K.-Q. Gu, V.L. Kharitonov, J. Chen. Stability of time-delay systems, Birkhauser, Basel,2003.
[43] Z.-H. Guan, H. Zhang. Stabilization of complex network with hybrid impulsive and switch-ing control. Chaos Solitons & Fractals, 2008, 37:1372-1382.
[44] J.K. Hale. Theory of functional differential equations. Springer-Verlag, 1977.
[45] J.K. Hale, P.M. Amorez. Stability in neutral equations. Nonlinear Analysis, 1977, 1: 161-173.
[46] J.K. Hale, S.M. VerduynLunel. Introduction to functional differential equations. New York:Springer-Verlag, 1993.
[47] Q.-L. Han. A descriptor system approach to robust stability of uncertain neutral systemswith discrete and distributed delays. Automatica, 2004, 40:1791-1796.
[48] Q.-L. Han. On stability of linear neutral systems with mixed time delays: A discretizedLyapunov functional approach. Automatica, 2005, 47:1209-1218.
[49] Q.-L. Han. Robust stability of uncertain delay-differential systems of neutral type. Auto-matica, 2002, 38:719-723.
[50] Q.-L. Han. Robust stability for a class of linear systems with time-varying delay and non-linear perturbations. Computer and Mathematics with Applications, 2004, 47:1201-1209.
[51] Q.-L. Han. Stability of linear neutral systems with linear fractional norm-bounded uncer-tainty. American Control Conference, 2005:2827-2832.
[52] Q.-L. Han, K.-Q. Gu. On Robust Stability of Time-Delay Systems With Norm -BoundedUncertainty. IEEE transactions on automatic control, 2001, 46:1426-1432.
[53] Q.-L. Han, L. Yu. Robust stability of linear neutral systems with nonlinear parameter per-turbations, IEE Proceedings Control Theory & Applications, 2004, 151:539-546.
[54] Q.-L. Han, X.-H. Yu, K.-Q. Gu. On Computing the Maximum Time-Delay Bound for Sta-bility of Linear Neutral Systems. IEEE transactions on automatic control, 2004, 49:2281-2287.
[55] P. He, D.-Q. Cao. Algebraic stability criteria of linear neutral systems with multiple timedelays. Applied Mathematics and Computation, 2004,155:643-653.
[56] Y. He, M. Wu. On Delay- dependent Stability of Neutral Systems With Nonlinear Pertur-bations. Mathematical theory and applications, 2003, 3:91-96.
[57] Y. He, Q.-G. Wang, L. Xie, C. Lin. Further improvement of free-weighting matrices tech-nique for systems with time-varying delay. IEEE Transaction on Automatic Control, 2007,52:293-299.
[58] Y. He, Q.-G. Wang, C. Lin, M. Wu. Augmented Lyapunov functional and delay dependentstability criteria for neutral systems. International Journal of Robust Nonlinear Control.2005, 15:923-933.
[59] Y. He, M. Wu, J.-H. She. Delay-dependent robust stability criteria for uncertain neutralsystems with mixed delays. Systems & Control Letters, 2004, 51:57 -65.
[60] J.P. Hespanha. Stabilization through hybrid control. Encyclopedia of Life Support Systems(EOLSS),Control Systems, Robotics, and Automation. Oxford, UK, 2004.
[61] J.P. Hespanha. Uniform stability of switched linear systems: Extensions of Lasalle’s invari-ance principle. IEEE Transactions on Automatic Control, 2004, 49:470-482.
[62] J.P. Hespanha, A.S. Morse. Stability of switched systems with average dwell-time. In Proc.38th IEEE Conference Decision Control, 1999:2655-2660.
[63] R. Horowitz, P. Varaiya. Control design of an automated highway system. Proceedings ofIEEE, 2000, 88:913-925.
[64] G.-D. Hu, G.-D. Hu, B. Cahlon. Algebraic criteria for stability of linear neutral systemswith a single delay. Journal of Computational and Applied Mathematics, 2001, 135:125-133.
[65] G.-D. Hu, G.-D. Hu. Some simple stability criteria of neutral delay-differential systems.Applied Mathematics and Computation, 1996, 80:257-271.
[66] K. Ito, T.J. Tarn. A linear quadratic optimal control for neutral systems. Nonlinear Analysis,1985, 9:699-727.
[67] H.R. Karimi, M. Zapateiro, N.S. Luo. Stability analysis and control synthesis of neutralsystems with time-varying delays and nonlinear uncertainties. Chaos, Solitons & Fractals,2009, 42:595-603.
[68] D.Y. Khusainow, E.A. Yunkova. Investigation of the stability of linear-systems of neutraltype by the Lyapunov function menthod. Differential Equations, 1988, 24:424-431.
[69] S. Kim, S.A. Campbell, X.-Z. Liu. Stability of a class of linear switching systems with timedelay. IEEE Trans. on Circuits and Systems-I: Regular Papers, 2006, 53:384-393.
[70] V.B. Kolmanovskii, J.P. Richard. Stability of some linear systems with delays. IEEE Trans-actions on Automatic Control, 1999, 44:984-989.
[71] J. Lam, H. Gao, C. Wang. Stability analysis for continuous systems with two additive time-varying delay components. Systems & Control Letters, 2007, 56: 16-24.
[72]李宏飞,罗学波.具有非线性扰动的中立型系统的鲁棒稳定性.西南师范大学学报(自然科学版), 2004, 4:539-545.
[73]廖晓昕.稳定性的理论、方法和应用.武汉:华中科技大学出版社, 2002, 42-65.
[74] L.S. Lasdon. Optimization Theory for Large Scale Systems, Series of Operation Research,MacMillan, New York, 1970.
[75] H. Li, H.-B. Li, S.-M. Zhong. Some new simple stability criteria of linear neutral systemswith a single delay. Journal of Computational and Applied Mathematics, 2007, 200:441-447.
[76] H. Li, H.-B. Li, S.-M. Zhong. Stability of neutral type descriptor system with mixed delays.Chaos,solitions & Fractals, 2007, 5:1796-1800.
[77] P. Li, S.-M. Zhong. BIBO stabilization for system with multiple mixed delays and nonlinearperturbations, Applied Mathematics and Computation, 2008, 196:207-213.
[78] P. Li, S.-M. Zhong. BIBO stabilization of time-delayed systemwith nonlinear perturbation.Applied Mathematics and Computation, 2008, 195:264-269.
[79] P. Li, S-M. Zhong. BIBO stabilization of piecewise switched linear systems with delaysand nonlinear perturbations. Applied Mathematics and Computation, 2009, 213:405-410.
[80] P. Li, S-M. Zhong, J.-Z. Cui. Stability analysis of linear switching systems with time delays.Chaos, Solitons & Fractals, 2009, 40:474-480.
[81] R.-H. Li, Y.-M. Hou. Convergence and stability of numerical solutions to SDDEs withMarkovian switching. Applied Mathematics and Computation, 2006, 175:1080-1091.
[82]李顺洋,田彦涛. Markov切换系统的随机稳定性分析.控制工程, 2004, 11:325-327
[83] D. Liberzon. Switching in Systems and Control. Birkhauser, Boston, 2003.
[84] D. Liberzon, J.P. Hespanha, A.S. Morse. Stability of switched linear systems: A Lie-algebraic condition. System & Control Letter, 1999, 37:117-122.
[85] D. Liberzon, A.S. Morse. Basic problems in stability and design of switched systems. IEEEControl Systems Magazine, 1999, 19:59-70.
[86] D. Liberzon, R. Tempo. Common Lyapunov functions and gradient algorithms. IEEETransactions on Automatic Control, 2004, 49:990-994.
[87] C.-H. Lien. Asymptotic criterion for neutral systems with multiple time-delays. ElectronicsLetters, 1999,35:850-852.
[88] C.-H. Lien, K.-W Yu, J.G. Hsieh. Stability conditions for a class of neutral systems withmultiple time delays. Journal of Mathematical Analysis and Applications, 2000, 245:20-27.
[89] H. Lin, P.J. Antsaklis. Stability and stabilizability of switched linear systems: a short sur-veyof recent results. Proceedings of the 2005 IEEE International Symposium on IntelligentControl, 2005:24-29.
[90] H. Lin, P.J. Antsaklis. Stability and Stabilizability of Switched Linear Systems: A Surveyof Recent Results. IEEE Transactions on Automatic Control, 2009, 54:308-322.
[91] D.-Y. Liu, X.-Z. Liu, S.-M. Zhong. Delay-dependent robust stability and control synthe-sis for uncertain switched neutral systems with mixed delays. Applied Mathematics andComputation, 2008, 202:828-839.
[92] D.-Y. Liu, S.-M. Zhong, L.-L. Xiong. On robust stability of uncertain neutral systems withmultiple delays. Chaos, Solitons & Fractals, 2009, 39:2332-2339.
[93] X.-G. Liu, M. Wu, R. Martin. Delay-dependent stability analysis for uncertain neutral sys-tems with time-varying delays. Mathematics and Computers in Simulation, 2007, 75:15-27.
[94] X.-G. Liu, M. Wu, R. Martin, M.-L. Tang. Stability analysis for neutral systems with mixeddelays. Journal of Computational and Applied Mathematics, 2007, 202:478-497.
[95] X.-Z. Liu, K.L. Teo, H.-T. Zhang, G.-R. Chen. Switching control of linear systems forgenerating chaos. Chaos Solitons & Fractals, 2006, 30:725–733.
[96] Y. Liu, F. Wang. Razumikhin-Lyapunov functional method for the stability of impulsiveswitched systems with time delay. Mathematical and Computer Modelling, 2009, 49:249-264.
[97] C. Livadas, J. Lygeros, N.A. Lynch. High-level modeling and analysis of the traffic alertand collision avoidance system. Proceedings of IEEE, 2000, 88:926-948.
[98] J.L. Mancilla-Aguilar, R.A. Garc′?a. A converse Lyapunov theorem for nonlinear switchedsystems. Systems & Control Letters, 2000, 41:67-71.
[99] M. Margaliot. A counterexample to a conjecture of gurvits on switched systems. IEEETransaction on Automatic Control, 2007, 52:1123-1126.
[100] O. Mason, R. Shorten. The geometry of convex cones associated with the Lyapunov in-equality and the common Lyapunov function problem. Electronic Journal of Linear Alge-bra, 2005, 12:42-63.
[101] G. Michaletzky, L. Gerencser. BIBO stability of linear switching systems. IEEE Transac-tions on Automatic Control, 2002, 47:1895-1898.
[102] A.N. Michel. Recent trends in the stability analysis of hybrid dynamical systems. IEEETransactions on Circuits System(I), 1999, 46:120-134.
[103] Y.-S. Moon. Robust control of time-delay system using linear matrix inequalities. Ph.D.Thesis, Seoul National University, 1998.
[104] K.S. Narendra, J. Balakrishnan. A common Lyapunov function for stable LTI systems withcommuting A-matrices. IEEE Transactions on Automatic Control, 1994, 39:2469-2471.
[105] B. Ni, Q.-L. Han. On stability for a Class of Neutral Delay-Differential systems.Pro.American Control Conference, Arington, 2001:4544-4549.
[106]倪涛洋,黎培兴,李彩霞.中立型线性微分方程的稳定性. 2005, 1:144-147.
[107] S.L. Niculescu. Optimizing model transformations in delay-dependent analysis of neutralsystems. Nonlinear Analysis, 2001, 47:5379-5390.
[108] S.L. Niculescu. Further remarks on delay-dependent stability of linear neutral systems. Pro-ceeding of MTNS, 2000:4368-4372.
[109] S.L. Niculescu. On Delay-dependent stability in Neutral systems. Proceeding of AmericanControl Conference, Arlington, 2001:3384-3388.
[110] C.-H. Lien, K.-W. Yu, J.G. Hsieh. Stability conditions for a class of neutral systems withmultiple time delays. Journal of Mathematical Analysis and Application, 2000, 245:20-27.
[111] A. Papachristodoulou, S. Prajna. A tutorial on sum of squares techniques for systems anal-ysis. In Proceeding of 2005 American Control Conference, 2005.
[112] J.H. Park. A new delay-dependent criterion for neutral systems with multiple delays. Jour-nal of Computational and Applied Mathematics, 2001,136:177-184.
[113] J.H. Park. Novel robust stability criterion for a class of neutral systems with mixed delaysand nonlinear perturbations. Applied Mathematics and Computation, 2005, 161:413-421.
[114] J.H. Park. Robust guaranteed cost control for uncertain linear differential systems of neutraltype. Applied Mathematics and Computation, 2003, 140:523-535.
[115] J.H. Park. Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments. Mathematics and Computers in Simulation, 2002, 59:401-412.
[116] J.H. Park, H.Y. Jung. On the exponential stability of a class of nonlinear systems includingdelayed perturbations. Journal of Computational and Applied Mathematics, 2003, 159:467-471.
[117] J.H. Park, O. Kwon. On new stability criterion for delay-differential systems of neutral type.Applied Mathematics and Computation, 2005, 162:627-637.
[118] J.H. Park, O. Kwon. On guaranteed cost control of neutral systems by retarded integral statefeedback. Applied Mathematics and Computation, 2005,165:393-404.
[119] J.H. Park, S.Won. Stability analysis for neutral delay-differential systems. Journal of theFranklin Institute, 2000,337:1-9.
[120] J.H. Park, S. Won. Asymptotic Stability of Neutral Systems with Multiple Delays. Journalof optimization theory and applications, 1999, 103:183-200.
[121] P. Park. A delay-dependent stability criterion for systems with uncertain time-invariant de-lays. IEEE Transactions on Automatic Control, 1999,44:876-877.
[122] J.R. Partington, C. Bonnet. H∞and BIBO stabilization of delay systems of neutral type.Systems & Control Letters, 2004, 52:283-288.
[123] S. Pettersson, B. Lennartson. Hybrid system stability and robustnessverification using linearmatrix inequalities. International journal of Control, 2002, 75:1335-1355.
[124] D. Pepyne, C. Cassandaras. Optimal control of hybrid systems in manufacturing. Proceed-ings of IEEE, 2000, 88:1008-1122.
[125] S. Prajna, A. Papachristodoulou. Analysis of switched and hybrid systems beyond piece-wise quadratic methods. Proceeding of 42nd IEEE Conference of Decision Control,2003:2779-2784.
[126] M.D. Sen, J.L. Malaina, A. Gallego, J.C. Soto. Stability of non-neutral and neutral dynamicswitched systems subject to internal delays. American Journal of Applied Sciences, 2005,2:1481-1490.
[127] M. Slemrod, E.F. Infante, Asymptotic stability criteria for linear systems of differentialequations of neutral type and their discrete analogues. Journal of Mathematical Analysisand Application, 1972, 38:399-415.
[128] M. Song, T. Tran, N. Xi, Integration of task scheduling, action planning, and control inrobotic manufacturing systems. Proceedings of IEEE, 2000, 88:1097-1107.
[129] M.-H. Sun, James Lam, S.-Y. Xu, Y. Zou. Robust exponential stabilization for Markovianjump systems with mode-dependent input delay. Automatica, 2007, 43:1799-1807.
[130] X.-M. Sun, J. Fu, H.-F. Sun, J. Zhao, Stability of linear switched neutral delay systems.Proceedings of The Chinese Society for Electrical Engineering, 2005, 25:42-46.
[131] X.-M. Sun, J. Zhao, D.J. Hill, Stability and L2-gain analysis for switched delay systems: Adelay-dependent method. Automatica, 2006, 42:1769-1774.
[132] Y.-G. Sun, L. Wang, G. Xie. Stability of switched systems with time-varying delays: de-laydependentcommon Lyapunov functional approach. Proceedings of the 2006 AmericanControl Conference, 2006:1544-1549.
[133] Z.-D. Sun, Stabilizability and Insensitivity of Switched Linear Systems. IEEE Transactionson Automatic Control, 2004, 49:1133-1137.
[134] Z.-D. Sun, S.S. Ge, Analysis and synthesis of switched linear control systems. Automatica,2005, 41:181-195.
[135] Z.-D. Sun, S.S. Ge, Switched Linear Systems: Control and Design. London: Springer-Verlag, 2005.
[136] J.-K. Tian, L.-L. Xiong, J.-X. Liu, X.-J. Xie, Novel delay-dependent robust stability criteriafor uncertain neutral systems with time-varying delay. Chaos, Solitons & Fractals, 2009,40:1858-1866.
[137] M.G. Todorov, M.D. Fragoso, Output feedback h∞control of continuous-time infinitemarkovian jump linear systems via LMI methods. SIAM Journal Control optimal, 2008,47:950-974.
[138] F.-H. Tu, X.-F. Liao, W. Zhang. Delay-dependent asymptotic stability of a two-neuron sys-tem with different time delays, Chaos, Solitons & Fractals, 2006, 2: 437-447.
[139] H.-L. Xu, X.-Z. Liu, K.L. Teo. A LMI approach to stability analysis and synthesis of im-pulsive switched systems with time delays. Nonlinear Analysis: Hybrid Systems, 2008,2:38-50.
[140] P. Varaiya, Smart cars on smart roads: Problems of control. IEEE Transactions on Auto-matic Control, 1993, 38:195-207.
[141] M. Vidyasagar, Nonlinear systems analysis(2nd ed). Upper Saddle River, NJ, USA:Prentice-Hall, Inc., 1992.
[142] R. Wang, M. Liu, J. Zhao. Reliable H∞control for a class of switched nonlinear systemswith actuator failures. Nonlinear Analysis: Hybrid Systems, 2007, 1:317-325.
[143] H. Wu, K. Mizukami. Robust stabilization of uncertain linear dynamical systems. Interna-tional Journal of Systems Science, 1993, 24:265-276.
[144] G.-M. Xie, L. Wang, Controllability and stabilizability of switched linear-systems. Systems& Control Letters, 2003, 48:135-155.
[145] G.-M. Xie, L. Wang. Reachability realization and stabilizability of switched linear discrete-time systems. Journal of Mathematical Analysis and Applications, 2003, 280:209-220.
[146] L. Xie. Output feedback H∞control of systems with parameter uncertainty. InternationalJournal Control, 1996, 63:741-750.
[147] J.-L. Xiong, James Lam, H.-J. Gao, DanielW.C. Ho. On robust stabilization of Markovianjump systems with uncertain switching probabilities. Automatica, 2005, 41:897-903.
[148] L.-L. Xiong, S.-M. Zhong, J.-K. Tian. Novel robust stability criteria of uncertain neutralsystems with discreteand distributed delays. Chaos, Solitons & Fractals, 2009, 40:771-777.
[149] W.-J. Xiong , J.-L. Liang. Novel stability criteria for neutral systems with multiple timedelays. Chaos,solitions & Fractals, 2007, 5:1735-1741.
[150] D.-Y. Xu, S.-M. Zhong. Robust BIBO stabilization of linear large-scale systems with non-linear delay perturbations, Dynamics of Continuous, Discrete and Impulsive Systems, 1996,2:511-520.
[151] D.-Y. Xu, S.-M. Zhong, M. Li. BIBO stabilization of large-scale systems, Control Theoryand Applications, 1995, 12:758-763.
[152] V.A. Yakubovich, S-procedure in nonlinear control theory. Vestnik. Leningradskogo Uni-versiteta, Ser. Matematika, Series1, 62-77.
[153] J. Yang, S.-M. Zhong, L.-L. Xiong, A descriptor system approach to non-fragile H∞con-trol for uncertain fuzzy neutral systems, Fuzzy Sets and Systems, 2009, 160:423-438.
[154] B. Yang, T. Li, Y.- H. Jiang. On the stability of neutral systems with multiple delays. Amer-ican control conference, 2003:5066-5067.
[155] B. Yang, R.J. Zhu, T. Li. Delay-dependent stability criterion for a class of neutral time delaysystems. Proceedings of the American Control Conference, 2003:2694-2697.
[156] H. Ye, A.N. Michel, K.-N. Wang. Robust stability of Linear Time-Delay systems: Retardedand Neutral Types. IEEE Transactions on Automatic Control,1995,40:1488-1491.
[157] D. Yue, S. Won, O. Kwon. Delay dependent stability of neutral systems with time delay: anLMI approach. IEE Proceedings, 2003, 150:23-27.
[158] G.-S. Zhai, B. Hu, K. Yasuda, A.N. Michel. Disturbance attenuation properties of time-controlled switched systems. Journal of Franklin Institute, 2001, 338:765–779.
[159] G.-S. Zhai, B. Hu, K. Yasuda, A.N. Michel. Qualitative analysis of discrete-time switchedsystems. Proceedings of 2002 American Control Conference, 2002:1880-1885.
[160] G.-S. Zhai, H. Lin. Controller failure time analysis for symmetric H1 control systems. In-ternational journal of control, 2004, 77:598-605.
[161] G.-S. Zhai, X.-P. Xu, H. Lin, A.N. Michel. Analysis and design of switched normal systems.Nonlinear Analysis: Theory, Methods & Applications, 2006, 65:2248-2259.
[162] K.-Y. Zhang, D.-Q. Cao. Further results on asymptotic stability of linear neutral systemswith multiple delays. Journal of the Franklin Institute, 2007, 344:858-866.
[163]张发明.中立型时滞系统的渐近稳定性.湘潭大学自然科学学报, 2002,4:92-96.
[164]张克,跃杨苏.线性中立型时滞系统的稳定性判据.西南交通大学学, 2006, 3:386-381.
[165] W.-A. Zhang, L. Yu, Delay-dependent Robust Stability of Neutral Systems with MixedDelays and Nonlinear Perturbations. Acta Automatica Sinica, 2007, 33:863-866.
[166]张先明,吴敏,何勇.中立型线性时滞系统的时滞相关稳定性.自动化学报, 2004,30:624-628.
[167] Y.-P. Zhang, X.-Z, Liu, H. Zhu, Stability analysis and control synthesis for a class ofswitched neutral systems. Applied Mathematics and Computation, 2007, 190:1258-1266.
[168]张先明,吴敏,何勇.中立型时滞系统得时滞相关稳定性.自动化学报, 2004, 30:624-628.
[169] Y.-P. Zhang, X.-Z. Liu, H. Zhu. Stability analysis and control synthesis for a class ofswitched neutral systems. Applied Mathematics and Computation, 2007, 190:1258-1266.
[170] J. Zhao, J.H. David. On stability, L2-gain and H∞control for switched systems, Automat-ica, 2008, 44:1220-1232.
[171] J. Zhao, G.M. Dimirovski. Quadratic stability of a class of switched nonlinear systems.IEEE Transaction on Automatic Control, 2004, 49:574-578.
[172] Z.-R. Zhao, W. Wang, B. Yang. Delay and its time-derivative dependent robust stability ofneutral control system. Applied Mathematics and Computation, 2007, 187:1326-1332.
[173]曾铭涛,桂卫华,唐朝晖.一类变时滞中立型系统的全局指数稳定性研究.计算机工程与科学, 2005, 27:77-81.
[174] S.-S. Zhou, J. Lam, Robust stabilization of delayed singular systems with linear fractionalparametric uncertainties. Circuits Systems Signal Processing, 2003, 22:579-588.
[175] Z. Zou, Y. Wang. New stability criterion for a class of linear systems with time-varyingdelay and nonlinear perturbations, IEE Proceedings of Control Theory and Applications,2006, 153:623-626.