几类时滞切换系统的鲁棒控制
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摘要
切换系统作为一类重要的混杂系统,能够描述工业生产过程中的许多具有连续动态特性和离散动态特性的复杂控制系统;多控制器切换控制技术能够为许多高度复杂的系统或具有大不确定性的系统提供有效的控制;以及计算机控制的发展极大地促进了人们对切换系统的研究。时滞现象广泛存在于各种工业生产过程中,它是导致系统不稳定或性能恶化的一个重要原因,因而有关时滞系统的研究引起了许多学者的广泛关注,成为控制领域和控制工程的热门课题。时滞切换系统是一种由连续动态、离散动态和时滞相互作用的复杂动态系统,这种复杂的动态特性使得对切换系统的分析和控制变得非常困难,因此,研究时滞切换系统的鲁棒控制问题具有重要意义。本文应用切换Lyapunov-Krasovskii泛函方法、线性矩阵不等式方法以及锥补线性化算法讨论了两类具有时变时滞的线性离散切换系统在满足给定H_∞性能指标下的鲁棒渐近稳定性,构造出满足给定H_∞性能指标的切换反馈控制器。最后通过数值实例说明本文所得结论的正确性和有效性。本文的主要工作如下:
第三章讨论了一类不确定时滞切换系统的鲁棒稳定性与状态反馈镇定问题。切换系统中各子系统的系数矩阵都含有范数有界时变不确定性。应用完全切换Lyapunov-Krasovskii泛函方法,给出在任意切换信号下使得此类不确定性时滞切换系统镇定的状态反馈控制器的两种构造条件。两种条件均是时滞相关的,第一种条件具有线性矩阵不等式形式,第二种条件是非线性的,利用锥补线性化算法给出求此非线性不等式的一种迭代算法。所得控制器不仅使相应的闭环系统渐近稳定,而且使得闭环系统的性能满足给定的H_∞指标。最后通过数值实例将本文所得稳定性条件与文献[9]中相关结论比较,说明本文所得结论具有更低的保守性;通过数值实例比较本文所得两类控制器构造方法,验证了第一种构造条件具有明显优势。
第四章讨论了一类具有范数有界型不确定性的多时滞线性离散切换系统的鲁棒动态输出反馈控制问题。利用切换Lyapunov-Krasovskii泛函方法得到在任意切换序列下,构造动态输出反馈控制律的充分条件,所得控制器能够使相应的闭环系统鲁棒渐近稳定。结论中的矩阵不等式条件是时滞相关且非线性的。应用锥补线性化思想将此非线性矩阵不等式的可行性问题转化为一个受线性矩阵不等式约束的非线性规划问题,并给出求此非线性规划问题的一种迭代算法。
As an important class of hybrid systems, the switched systems can be used to model many actual complex control systems with continuous dynamics and discrete dynamics in industrial processes; Multi-controller switching control technology can effectively cope with highly complex systems or systems with large uncertainties and the progress of computer control technology immensely promote the study of control systems. Time delay presences widespread in various industrial processes, and is the main source of instability and poor performances of control systems, so the study on time delay systems have received considerable attention by many researchers, and became a hot issue in control areas and control engineering. Time-delay switched systems is a class of complex dynamic systems with the interaction of continuous dynamics and discrete dynamics and time delays which make the analysis and control of switched systems difficult, hence the study on robust control of switched systems with time delays is of great significance. Based on the switched Lyapunov-Krasovskii functions, linear matrix inequality technology, the cone complementary linearization algorithm, this dissertation investigates the asymptotic stability of two classes of linear discrete-time switched system with time-varying delays under a given H_∞performance, construct the switched feedback controllers which meet the given H_∞performance. Finally, several numerical examples are given to illustrate the correctness and validity of the proposed results. The main work and research results of this thesis lie in the following:
Chapter 3 investigates the robustly stability and state-feedback stabilization for a class of linear discrete-time switched systems with time-varying delays. The system matrixes of all sub-systems, are norm bounded and time-varying. By applying full switched Lyapunov-Krasovskii function method, two sufficient conditions constructing the state-feedback controller are given for the underlying system under arbitrary switched signals. All the conditions are delay-dependent, the first condition is in terms of LMI, and the second one is nonlinear, an iterative algorithm is given by cone complementary linearization algorithm. The obtained controller not only guarantee the corresponding closed-loop system asymptotically stable, but also a prescribed H_∞noise-attenuation level bound is guaranteed. Finally, a numerical example is given to compare the result with previous results in [9] and illustrate our results with less conservative, another example is given to compare the two methods of constructing state-feedback controller and illustrate the first method is better than the second one.
Chapter 4 concern with the output-feedback control of uncertain linear discrete-time switched systems with multiple time-varying delays, the uncertainty is norm-bounded. By applying switched Lyapunov-Krasovskii function method, the sufficient conditions of constructing the output feedback controller of multiply time-delay switched systems under arbitrary switch signals is given. The obtained controller not only guarantee the corresponding closed-loop system asymptotic stable, but also a prescribed H_∞noise-attenuation level bound is guaranteed. The obtained condition is delay-dependent but nonlinear. The cone complementary linearization algorithm is used to transform the feasibility problem of the nonlinear matrix inequalities into a nonlinear program problem subject to linear matrix inequalities,and an iterative algorithm is given to solve this nonlinear program problem.
第三章讨论了一类不确定时滞切换系统的鲁棒稳定性与状态反馈镇定问题。切换系统中各子系统的系数矩阵都含有范数有界时变不确定性。应用完全切换Lyapunov-Krasovskii泛函方法,给出在任意切换信号下使得此类不确定性时滞切换系统镇定的状态反馈控制器的两种构造条件。两种条件均是时滞相关的,第一种条件具有线性矩阵不等式形式,第二种条件是非线性的,利用锥补线性化算法给出求此非线性不等式的一种迭代算法。所得控制器不仅使相应的闭环系统渐近稳定,而且使得闭环系统的性能满足给定的H_∞指标。最后通过数值实例将本文所得稳定性条件与文献[9]中相关结论比较,说明本文所得结论具有更低的保守性;通过数值实例比较本文所得两类控制器构造方法,验证了第一种构造条件具有明显优势。
第四章讨论了一类具有范数有界型不确定性的多时滞线性离散切换系统的鲁棒动态输出反馈控制问题。利用切换Lyapunov-Krasovskii泛函方法得到在任意切换序列下,构造动态输出反馈控制律的充分条件,所得控制器能够使相应的闭环系统鲁棒渐近稳定。结论中的矩阵不等式条件是时滞相关且非线性的。应用锥补线性化思想将此非线性矩阵不等式的可行性问题转化为一个受线性矩阵不等式约束的非线性规划问题,并给出求此非线性规划问题的一种迭代算法。
As an important class of hybrid systems, the switched systems can be used to model many actual complex control systems with continuous dynamics and discrete dynamics in industrial processes; Multi-controller switching control technology can effectively cope with highly complex systems or systems with large uncertainties and the progress of computer control technology immensely promote the study of control systems. Time delay presences widespread in various industrial processes, and is the main source of instability and poor performances of control systems, so the study on time delay systems have received considerable attention by many researchers, and became a hot issue in control areas and control engineering. Time-delay switched systems is a class of complex dynamic systems with the interaction of continuous dynamics and discrete dynamics and time delays which make the analysis and control of switched systems difficult, hence the study on robust control of switched systems with time delays is of great significance. Based on the switched Lyapunov-Krasovskii functions, linear matrix inequality technology, the cone complementary linearization algorithm, this dissertation investigates the asymptotic stability of two classes of linear discrete-time switched system with time-varying delays under a given H_∞performance, construct the switched feedback controllers which meet the given H_∞performance. Finally, several numerical examples are given to illustrate the correctness and validity of the proposed results. The main work and research results of this thesis lie in the following:
Chapter 3 investigates the robustly stability and state-feedback stabilization for a class of linear discrete-time switched systems with time-varying delays. The system matrixes of all sub-systems, are norm bounded and time-varying. By applying full switched Lyapunov-Krasovskii function method, two sufficient conditions constructing the state-feedback controller are given for the underlying system under arbitrary switched signals. All the conditions are delay-dependent, the first condition is in terms of LMI, and the second one is nonlinear, an iterative algorithm is given by cone complementary linearization algorithm. The obtained controller not only guarantee the corresponding closed-loop system asymptotically stable, but also a prescribed H_∞noise-attenuation level bound is guaranteed. Finally, a numerical example is given to compare the result with previous results in [9] and illustrate our results with less conservative, another example is given to compare the two methods of constructing state-feedback controller and illustrate the first method is better than the second one.
Chapter 4 concern with the output-feedback control of uncertain linear discrete-time switched systems with multiple time-varying delays, the uncertainty is norm-bounded. By applying switched Lyapunov-Krasovskii function method, the sufficient conditions of constructing the output feedback controller of multiply time-delay switched systems under arbitrary switch signals is given. The obtained controller not only guarantee the corresponding closed-loop system asymptotic stable, but also a prescribed H_∞noise-attenuation level bound is guaranteed. The obtained condition is delay-dependent but nonlinear. The cone complementary linearization algorithm is used to transform the feasibility problem of the nonlinear matrix inequalities into a nonlinear program problem subject to linear matrix inequalities,and an iterative algorithm is given to solve this nonlinear program problem.
引文
[1] D. Liberzon, A.S. Morse. Basic problems in stability and design of switched systems[J]. IEEE Control Systems Magazine, 1999, 19(5): 59-70.
[2] K.S. Narendra, J. Balakrishnan. A common Lyapunov function for stable LTI systems with commuting A-matrices[J]. IEEE Transactions on Automatic Control, 1994, 39(12): 2469-2471.
[3] R. Shorten, K. Narendra. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for two stable second order linear time-invariant systems[C]. Proceedings of the 1999 American Control Conference, 1999, pp. 1410-1414.
[4] R. Shorten, K. Narendra. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable LTI systems[J]. International Journal of Control of Adaptive Control and Signal Processing, 2002, 16(10): 709-728.
[5] C. King, R. Shorten. A singularity test for the existence of common quadratic Lyapunov functions for pairs of stable LTI systems[C]. Proceedings of the 2004 American Control Conference, 2004, pp. 3881-3884.
[6] W. Dayawansa, C.F. Martin. A converse Lyapunov theorem for a class of dynamical systems with undergo switching[J]. IEEE Transactions on Automatic Control, 1999, 44(4): 751-760.
[7] J.L. Mancilla-Aguilar, R. A. Garcia. A converse Lyapunov theorem for nonlinear switched systems[J]. Systems & Control Letters, 2000, 41(1): 67-71.
[8] J. Daafouz, P. Riedinger, C. Iung. Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach[J]. IEEE Transactions on Automatic Control, 2002, 47(11): 1883-1887.
[9] L. Zhang, P. Shi, E.K. Boukas. H_∞output-feedback control for switched linear discrete-time systems with time-varying delays[J]. International Journal of Control, 2007, 80(8): 1354-1365.
[10] L.X. Zhang, C.H. Wang, L.J. Chen. Stability and stabilization of a class of multimode Linear discrete-time systems with polytopic uncertainties[J]. IEEE Transactions on Automatic Control, 2009, 56(9): 3684-3692.
[11] L.X. Zhang, P. Shi, E.K. Boukas, C. Wang. Robust l_2-l_∞filtering for switched linear discrete time-delay systems with polytypic uncertainties[J]. IET Control Theory & Applications, 2007, 1(3): 722-730.
[12] M.S. Mahmoud. Delay-dependent H_∞filtering of a class of switched discrete-time state delay systems[J]. Signal Processing, 2008, 88(11): 2709-2719.
[13] D.S. Du, B. Jiang, P. Shi, S.S. Zhou. H_∞filtering of discrete-time switched systems with state delays via switched Lyapunov function approach[J]. IEEE Transactions on Automatic Control, 2006, 52(8): 1520-1525.
[14] D.S. Du, B. Jiang, P. Shi, S.S. Zhou. Robust l_2-l_∞control for uncertain discrete-time switched systems with delays[J]. Circuits Systems Signal Processing, 2006, 25(6): 729-744.
[15] M.S. Mahmoud, P. Shi, A.W.A. Saif. Stabilization of linear switched delay systems: H 2and H_∞methods[J]. Journal of Optimization Theory and Applications, 2009, 142(3): 583-601.
[16] X.W. Liu. Stability analysis of switched positive systems: A switched linear copositive Lyapunov function method [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2009, 56(5): 414-418.
[17] Y. Wang, W. Wang, D. Wang. LMI approach to design fault detection filter for discrete-Time switched systems with state delays[J]. International Journal of Innovative Computing, Information and Control, 2010, 6(1): 387-397.
[18] A. Morse. Supervisory control of families of linear set-point controllers part I: Exact matching[J]. IEEE Transactions on Automatic Control, 1996, 41(10): 1413-1431.
[19] P. Peleties, R.A. DeCarlo. Asymptotic stability of m-switched systems using Lyapunov-like functions[C]. Proceedings of the 1991 American Control Conference, 1991, pp. 1679-1684.
[20] M.S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid system[J]. IEEE Transactions on Automatic Control, 1998, 43(4): 475-482.
[21] M.S. Branicky. Stability of switched and hybrid systems[C]. IEEE conference on decision and control, 1997, pp: 120-125.
[22] L. Hou, A.N. Michel, H. Ye. Stability analysis of switched systems[C]. Proc.35rd conf. Decision and control, 1996, pp: 1208-1212.
[23] S. Pettersson, B. Lennartson. Stability and robustness for hybirdsystems[C]. Proc.35rd conf. Decision and control, 1996, pp: 1202-1207.
[24] H. Ye, A.N. Michel, L. Hou. Stability theory for hybrid dynamical systems[J]. IEEE Transactions on Automatic Control, 1998, 43(4): 461-474.
[25] J.P. Hespanha, A.S. Morse. Stability of switched systems with average dwell-Time[C]. Proc.38rd conf. Decision and control, 1999, pp: 1202-1207.
[26] G.S. Zhai, B. Hu, K. Yasuda, Anthony N. Michel. Piecewise Lyapunov functions for switched systems with average dwell Time[J]. Asian Journal of Control, 2001, 2(3): 192-197.
[27] G.S. Zhai, B. Hu, K. Yasuda, A.N. Michel. Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach[J]. International Journal of Systems Science, 2001, 32(8): 1055-1061.
[28] X.M. Sun, J. Zhao, D.J. Hill. Stability and L_2 -gain analysis for switched delay systems: A delay-dependent method [J]. Automatica, 2006, 42(10): 1769-1774.
[29] R. Wang, J. Zhao. Exponential stability analysis for discrete-time switched linear systems with time-delay[J]. International Journal of Innovative Computing, Information and Control, 2007, 3(6): 1557-1564.
[30] Z.R. Xiang, W.M. Xiang. Stabilization of a class of switched nonlinear systems with average dwell time[J]. WCICA 2008. 7th World Congress on Intelligent Control and Automation, 2008, pp:1673– 1676.
[31] M. Wang, G.M. Dimirovski, J. Zhao. Robust tracking control of a class of nonlinear switched systems: An average dwell-time method[C], 2009 American Control Conference Hyatt Regency Riverfront, 2009, pp: 1983-1787.
[32] L.X. Zhang, P. Shi. l_2 - l_∞model reduction for switched LPV systems with average dwell time[J]. IEEE Transactions on Automatic Control, 2008, 53(10): 2443– 2448.
[33] D. Ma, J. Zhao. Stabilization of networked control systems via switching controllers: An average dwell time approach[J]. The Sixth World Congress on Intelligent Control and Automation, 2006, pp: 4611-4622.
[34] L. Wu, T. Qi, Z. Feng. Average dwell time approach to L_2 - L_∞control of switched delay systems via dynamic output feedback[J]. IET Control Theory and Applications, 2009, 3(10): 1425– 1436.
[35] D.W. Ding, G.H. Yang. H_∞static output feedback control for discrete-time switched linear systems with average dwell time[J]. IET Control Theory and Applications, 2010, 4(3): 381– 390.
[36] M.A. Wicks, P. Peleties, A. DeClarlo. Switched controller synthesis for the quadratic stabilization of q pair of unstable linear systems[J]. European Journal of Control, 1998, 4: 140-147.
[37] M.A. Wicks, P. Peleties, A. DeClarlo. Construction of piecewise Lyapunov function for stabilizing switched systems[C]. Process 33th Conf. Decision And Control , 1994, pp: 3492-3497.
[38] E. Feron. Quadratic stabilizability of switched systems via state and output feedback[C]. Technical report CICS-P-468, MIT, 1996, submitted to SIAM J.control .Optimization.
[39] Z. Sun. Analysis and synthesis of switched linear control systems[J]. IEEE Transactions on Automatic Control, 2004, 49(7): 1133-1137.
[40] X. Xu, P.J. Antsaklis. Stabilizability of second-order LTI switched systems[J]. International Journal of Control, 2000, 73(14): 1261-1279.
[41] Z.J. Ji. Number of switchings and design of switching sequences for controllability of switched linear systems[C]. Chinese Control Conference , 2006, pp: 1049-1054.
[42] Z.J. Ji, L. Wang, X.X. Guo. Design of switched sequences of controllability realization of switched linear systems[J]. Automica, 2007, 43(4): 662-668.
[43] L.X. Zhang, C.H. Wang, L.J. Chen. Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties[J]. IEEE Transactions on Industrial Electronics, 2009, 56(9): 3684-3692.
[44] J.C. Geromal, G.S. Deaecto. Switched state feedback control for continuous time uncertain systems[J]. Automatic, 2009, 45(2): 593-597.
[45] W. Zhang, Alessandro Abate, Jianghai Hu, Michael P. Vitus. Exponential stabilization of discrete-time switched linear systems[J]. Automatica, 2009, 45(11): 2526-2536.
[46] R. Li, Z.G. Feng, K.L. Teo, G.R. Duan. Optimal piecewise state feedback control for impulsive switched systems[J]. Mathmatical And Computer Modelling, 2008, 48(3-4): 468-479.
[47] H. Lin, P.J. Antsaklis. Stability and stabilizability of switched linear systems: A short survey of recent results[C]. Proceedings of the 2005 IEEE international symposium on intelligent control limassol, Cyprus, 2009, pp: 24-29.
[48] Z.D. Sun, S.S. Ge. Analysis and synthesis of switched linear control systems[J]. Automatica, 2005, 41(2): 181-195.
[49]吴敏,何勇.时滞系统鲁棒控制——自由权矩阵方法[M].北京:科学出版社,2008:1-2.
[50] Y.S. Moon, P. Park, P. Kwon, W.H. kwon, Y.S. Lee. Delay-dependent robust stabilization of uncertain state delayed systems[J], International Journal of Control, 2001, 74(14): 1447-1455.
[51] M. Wang, Y. He, J.H. She, G.P. Liu. Delay-dependent criteria for robust stability of time-varying delay systems[J]. Automatica, 2004, 40(8): 1435-1439.
[52] Y. He, Q.G. Wang, L. Xie, C. Lin. Further improvement of free-weighting matrices technique for systems with time-varying delay[J]. IEEE Transactions on Automatic Control, 2007, 52(2): 647-650.
[53] Q.X. Chen, L. Yu, W.A. Zhang. Delay-dependent output feedback guaranteed cost control for uncertain discrete-time systems with multiple time-varying delays[J]. IET Control Theory Application, 2007, 1(1): 97-103.
[54] D. Wang, W. Wang, P. Shi. Delay-dependent exponential stability for switched delay systems[J]. Optimal Control Application and Methods, 2009, 30(4): 383-397.
[55]M.S. Mahmoud, F.M. Al-Sunni, Y. Shi. Switched discrete-time delay systems: Delay-dependent analysis and synthsis[J]. Circuits Syst Signal Process, 2009, 28(5): 735-761.
[56] L.E. Ghaoui, F. Oustry, M. AiRami. A Cone complementarity linearization algorithm for staticoutput-feedback and related problems[J]. IEEE Transactions on Automatic Control, 1997, 42(8): 1171-1176.
[57]俞立.鲁棒控制——线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002: 1-19.
[58] L. Xie, M. Fu, C.D. Souza. H∞control and quadratic stabilization of systems with parameter uncertainty via output feedback[J]. IEEE Transactions on Automatic Control, 1992, 37(8): 1253-1256.
[1] D. Liberzon, A.S. Morse. Basic problems in stability and design of switched systems[J]. IEEE Control Systems Magazine, 1999, 19(5): 59-70.
[2] K.S. Narendra, J. Balakrishnan. A common Lyapunov function for stable LTI systems with commuting A-matrices[J]. IEEE Transactions on Automatic Control, 1994, 39(12): 2469-2471.
[3] R. Shorten, K. Narendra. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for two stable second order linear time-invariant systems[C]. Proceedings of the 1999 American Control Conference, 1999, pp. 1410-1414.
[4] R. Shorten, K. Narendra. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable LTI systems[J]. International Journal of Control of Adaptive Control and Signal Processing, 2002, 16(10): 709-728.
[5] C. King, R. Shorten. A singularity test for the existence of common quadratic Lyapunov functions for pairs of stable LTI systems[C]. Proceedings of the 2004 American ControlConference, 2004, pp. 3881-3884.
[6] W. Dayawansa, C.F. Martin. A converse Lyapunov theorem for a class of dynamical systems with undergo switching[J]. IEEE Transactions on Automatic Control, 1999, 44(4): 751-760.
[7] J.L. Mancilla-Aguilar, R. A. Garcia. A converse Lyapunov theorem for nonlinear switched systems[J]. Systems & Control Letters, 2000, 41(1): 67-71.
[8] J. Daafouz, P. Riedinger, C. Iung. Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach[J]. IEEE Transactions on Automatic Control, 2002, 47(11): 1883-1887.
[9] L. Zhang, P. Shi, E.K. Boukas. H_∞output-feedback control for switched linear discrete-time systems with time-varying delays[J]. International Journal of Control, 2007, 80(8): 1354-1365.
[10] L.X. Zhang, C.H. Wang, L.J. Chen. Stability and stabilization of a class of multimode Linear discrete-time systems with polytopic uncertainties[J]. IEEE Transactions on Automatic Control, 2009, 56(9): 3684-3692.
[11] L.X. Zhang, P. Shi, E.K. Boukas, C. Wang. Robust l_2-l_∞filtering for switched linear discrete time-delay systems with polytypic uncertainties[J]. IET Control Theory & Applications, 2007, 1(3): 722-730.
[12] M.S. Mahmoud. Delay-dependent H_∞filtering of a class of switched discrete-time state delay systems[J]. Signal Processing, 2008, 88(11): 2709-2719.
[13] D.S. Du, B. Jiang, P. Shi, S.S. Zhou. H_∞filtering of discrete-time switched systems with state delays via switched Lyapunov function approach[J]. IEEE Transactions on Automatic Control, 2006, 52(8): 1520-1525.
[14] D.S. Du, B. Jiang, P. Shi, S.S. Zhou. Robust l_2-l_∞control for uncertain discrete-time switched systems with delays[J]. Circuits Systems Signal Processing, 2006, 25(6): 729-744.
[15] M.S. Mahmoud, P. Shi, A.W.A. Saif. Stabilization of linear switched delay systems: H 2and H_∞methods[J]. Journal of Optimization Theory and Applications, 2009, 142(3): 583-601.
[16] X.W. Liu. Stability analysis of switched positive systems: A switched linear copositive Lyapunov function method [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2009, 56(5): 414-418.
[17] Y. Wang, W. Wang, D. Wang. LMI approach to design fault detection filter for discrete-Time switched systems with state delays[J]. International Journal ofInnovative Computing, Information and Control, 2010, 6(1): 387-397.
[18] A. Morse. Supervisory control of families of linear set-point controllers part I: Exact matching[J]. IEEE Transactions on Automatic Control, 1996, 41(10): 1413-1431.
[19] P. Peleties, R.A. DeCarlo. Asymptotic stability of m-switched systems using Lyapunov-like functions[C]. Proceedings of the 1991 American Control Conference, 1991, pp. 1679-1684.
[20] M.S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid system[J]. IEEE Transactions on Automatic Control, 1998, 43(4): 475-482.
[21] M.S. Branicky. Stability of switched and hybrid systems[C]. IEEE conference on decision and control, 1997, pp: 120-125.
[22] L. Hou, A.N. Michel, H. Ye. Stability analysis of switched systems[C]. Proc.35rd conf. Decision and control, 1996, pp: 1208-1212.
[23] S. Pettersson, B. Lennartson. Stability and robustness for hybirdsystems[C]. Proc.35rd conf. Decision and control, 1996, pp: 1202-1207.
[24] H. Ye, A.N. Michel, L. Hou. Stability theory for hybrid dynamical systems[J]. IEEE Transactions on Automatic Control, 1998, 43(4): 461-474.
[25] J.P. Hespanha, A.S. Morse. Stability of switched systems with average dwell-Time[C]. Proc.38rd conf. Decision and control, 1999, pp: 1202-1207.
[26] G.S. Zhai, B. Hu, K. Yasuda, Anthony N. Michel. Piecewise Lyapunov functions for switched systems with average dwell Time[J]. Asian Journal of Control, 2001, 2(3): 192-197.
[27] G.S. Zhai, B. Hu, K. Yasuda, A.N. Michel. Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach[J]. International Journal of Systems Science, 2001, 32(8): 1055-1061.
[28] X.M. Sun, J. Zhao, D.J. Hill. Stability and L_2 -gain analysis for switched delay systems: A delay-dependent method [J]. Automatica, 2006, 42(10): 1769-1774.
[29] R. Wang, J. Zhao. Exponential stability analysis for discrete-time switched linear systems with time-delay[J]. International Journal of Innovative Computing, Information and Control, 2007, 3(6): 1557-1564.
[30] Z.R. Xiang, W.M. Xiang. Stabilization of a class of switched nonlinear systems with average dwell time[J]. WCICA 2008. 7th World Congress on Intelligent Control and Automation, 2008, pp:1673– 1676.
[31] M. Wang, G.M. Dimirovski, J. Zhao. Robust tracking control of a class of nonlinear switched systems: An average dwell-time method[C], 2009 American ControlConference Hyatt Regency Riverfront, 2009, pp: 1983-1787.
[32] L.X. Zhang, P. Shi. l_2 - l_∞model reduction for switched LPV systems with average dwell time[J]. IEEE Transactions on Automatic Control, 2008, 53(10): 2443– 2448.
[33] D. Ma, J. Zhao. Stabilization of networked control systems via switching controllers: An average dwell time approach[J]. The Sixth World Congress on Intelligent Control and Automation, 2006, pp: 4611-4622.
[34] L. Wu, T. Qi, Z. Feng. Average dwell time approach to L_2 - L_∞control of switched delay systems via dynamic output feedback[J]. IET Control Theory and Applications, 2009, 3(10): 1425– 1436.
[35] D.W. Ding, G.H. Yang. H_∞static output feedback control for discrete-time switched linear systems with average dwell time[J]. IET Control Theory and Applications, 2010, 4(3): 381– 390.
[36] M.A. Wicks, P. Peleties, A. DeClarlo. Switched controller synthesis for the quadratic stabilization of q pair of unstable linear systems[J]. European Journal of Control, 1998, 4: 140-147.
[37] M.A. Wicks, P. Peleties, A. DeClarlo. Construction of piecewise Lyapunov function for stabilizing switched systems[C]. Process 33th Conf. Decision And Control , 1994, pp: 3492-3497.
[38] E. Feron. Quadratic stabilizability of switched systems via state and output feedback[C]. Technical report CICS-P-468, MIT, 1996, submitted to SIAM J.control .Optimization.
[39] Z. Sun. Analysis and synthesis of switched linear control systems[J]. IEEE Transactions on Automatic Control, 2004, 49(7): 1133-1137.
[40] X. Xu, P.J. Antsaklis. Stabilizability of second-order LTI switched systems[J]. International Journal of Control, 2000, 73(14): 1261-1279.
[41] Z.J. Ji. Number of switchings and design of switching sequences for controllability of switched linear systems[C]. Chinese Control Conference , 2006, pp: 1049-1054.
[42] Z.J. Ji, L. Wang, X.X. Guo. Design of switched sequences of controllability realization of switched linear systems[J]. Automica, 2007, 43(4): 662-668.
[43] L.X. Zhang, C.H. Wang, L.J. Chen. Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties[J]. IEEE Transactions on Industrial Electronics, 2009, 56(9): 3684-3692.
[44] J.C. Geromal, G.S. Deaecto. Switched state feedback control for continuous time uncertain systems[J]. Automatic, 2009, 45(2): 593-597.
[45] W. Zhang, Alessandro Abate, Jianghai Hu, Michael P. Vitus. Exponential stabilization of discrete-time switched linear systems[J]. Automatica, 2009, 45(11): 2526-2536.
[46] R. Li, Z.G. Feng, K.L. Teo, G.R. Duan. Optimal piecewise state feedback control for impulsive switched systems[J]. Mathmatical And Computer Modelling, 2008, 48(3-4): 468-479.
[47] H. Lin, P.J. Antsaklis. Stability and stabilizability of switched linear systems: A short survey of recent results[C]. Proceedings of the 2005 IEEE international symposium on intelligent control limassol, Cyprus, 2009, pp: 24-29.
[48] Z.D. Sun, S.S. Ge. Analysis and synthesis of switched linear control systems[J]. Automatica, 2005, 41(2): 181-195.
[49]吴敏,何勇.时滞系统鲁棒控制——自由权矩阵方法[M].北京:科学出版社,2008:1-2.
[50] Y.S. Moon, P. Park, P. Kwon, W.H. kwon, Y.S. Lee. Delay-dependent robust stabilization of uncertain state delayed systems[J], International Journal of Control, 2001, 74(14): 1447-1455.
[51] M. Wang, Y. He, J.H. She, G.P. Liu. Delay-dependent criteria for robust stability of time-varying delay systems[J]. Automatica, 2004, 40(8): 1435-1439.
[52] Y. He, Q.G. Wang, L. Xie, C. Lin. Further improvement of free-weighting matrices technique for systems with time-varying delay[J]. IEEE Transactions on Automatic Control, 2007, 52(2): 647-650.
[53] Q.X. Chen, L. Yu, W.A. Zhang. Delay-dependent output feedback guaranteed cost control for uncertain discrete-time systems with multiple time-varying delays[J]. IET Control Theory Application, 2007, 1(1): 97-103.
[54] D. Wang, W. Wang, P. Shi. Delay-dependent exponential stability for switched delay systems[J]. Optimal Control Application and Methods, 2009, 30(4): 383-397.
[55]M.S. Mahmoud, F.M. Al-Sunni, Y. Shi. Switched discrete-time delay systems: Delay-dependent analysis and synthsis[J]. Circuits Syst Signal Process, 2009, 28(5): 735-761.
[56] L.E. Ghaoui, F. Oustry, M. AiRami. A Cone complementarity linearization algorithm for static output-feedback and related problems[J]. IEEE Transactions on Automatic Control, 1997, 42(8): 1171-1176.
[57]俞立.鲁棒控制——线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002: 1-19.
[58] L. Xie, M. Fu, C.D. Souza. H∞control and quadratic stabilization of systems withparameter uncertainty via output feedback[J]. IEEE Transactions on Automatic Control, 1992, 37(8): 1253-1256.
[2] K.S. Narendra, J. Balakrishnan. A common Lyapunov function for stable LTI systems with commuting A-matrices[J]. IEEE Transactions on Automatic Control, 1994, 39(12): 2469-2471.
[3] R. Shorten, K. Narendra. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for two stable second order linear time-invariant systems[C]. Proceedings of the 1999 American Control Conference, 1999, pp. 1410-1414.
[4] R. Shorten, K. Narendra. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable LTI systems[J]. International Journal of Control of Adaptive Control and Signal Processing, 2002, 16(10): 709-728.
[5] C. King, R. Shorten. A singularity test for the existence of common quadratic Lyapunov functions for pairs of stable LTI systems[C]. Proceedings of the 2004 American Control Conference, 2004, pp. 3881-3884.
[6] W. Dayawansa, C.F. Martin. A converse Lyapunov theorem for a class of dynamical systems with undergo switching[J]. IEEE Transactions on Automatic Control, 1999, 44(4): 751-760.
[7] J.L. Mancilla-Aguilar, R. A. Garcia. A converse Lyapunov theorem for nonlinear switched systems[J]. Systems & Control Letters, 2000, 41(1): 67-71.
[8] J. Daafouz, P. Riedinger, C. Iung. Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach[J]. IEEE Transactions on Automatic Control, 2002, 47(11): 1883-1887.
[9] L. Zhang, P. Shi, E.K. Boukas. H_∞output-feedback control for switched linear discrete-time systems with time-varying delays[J]. International Journal of Control, 2007, 80(8): 1354-1365.
[10] L.X. Zhang, C.H. Wang, L.J. Chen. Stability and stabilization of a class of multimode Linear discrete-time systems with polytopic uncertainties[J]. IEEE Transactions on Automatic Control, 2009, 56(9): 3684-3692.
[11] L.X. Zhang, P. Shi, E.K. Boukas, C. Wang. Robust l_2-l_∞filtering for switched linear discrete time-delay systems with polytypic uncertainties[J]. IET Control Theory & Applications, 2007, 1(3): 722-730.
[12] M.S. Mahmoud. Delay-dependent H_∞filtering of a class of switched discrete-time state delay systems[J]. Signal Processing, 2008, 88(11): 2709-2719.
[13] D.S. Du, B. Jiang, P. Shi, S.S. Zhou. H_∞filtering of discrete-time switched systems with state delays via switched Lyapunov function approach[J]. IEEE Transactions on Automatic Control, 2006, 52(8): 1520-1525.
[14] D.S. Du, B. Jiang, P. Shi, S.S. Zhou. Robust l_2-l_∞control for uncertain discrete-time switched systems with delays[J]. Circuits Systems Signal Processing, 2006, 25(6): 729-744.
[15] M.S. Mahmoud, P. Shi, A.W.A. Saif. Stabilization of linear switched delay systems: H 2and H_∞methods[J]. Journal of Optimization Theory and Applications, 2009, 142(3): 583-601.
[16] X.W. Liu. Stability analysis of switched positive systems: A switched linear copositive Lyapunov function method [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2009, 56(5): 414-418.
[17] Y. Wang, W. Wang, D. Wang. LMI approach to design fault detection filter for discrete-Time switched systems with state delays[J]. International Journal of Innovative Computing, Information and Control, 2010, 6(1): 387-397.
[18] A. Morse. Supervisory control of families of linear set-point controllers part I: Exact matching[J]. IEEE Transactions on Automatic Control, 1996, 41(10): 1413-1431.
[19] P. Peleties, R.A. DeCarlo. Asymptotic stability of m-switched systems using Lyapunov-like functions[C]. Proceedings of the 1991 American Control Conference, 1991, pp. 1679-1684.
[20] M.S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid system[J]. IEEE Transactions on Automatic Control, 1998, 43(4): 475-482.
[21] M.S. Branicky. Stability of switched and hybrid systems[C]. IEEE conference on decision and control, 1997, pp: 120-125.
[22] L. Hou, A.N. Michel, H. Ye. Stability analysis of switched systems[C]. Proc.35rd conf. Decision and control, 1996, pp: 1208-1212.
[23] S. Pettersson, B. Lennartson. Stability and robustness for hybirdsystems[C]. Proc.35rd conf. Decision and control, 1996, pp: 1202-1207.
[24] H. Ye, A.N. Michel, L. Hou. Stability theory for hybrid dynamical systems[J]. IEEE Transactions on Automatic Control, 1998, 43(4): 461-474.
[25] J.P. Hespanha, A.S. Morse. Stability of switched systems with average dwell-Time[C]. Proc.38rd conf. Decision and control, 1999, pp: 1202-1207.
[26] G.S. Zhai, B. Hu, K. Yasuda, Anthony N. Michel. Piecewise Lyapunov functions for switched systems with average dwell Time[J]. Asian Journal of Control, 2001, 2(3): 192-197.
[27] G.S. Zhai, B. Hu, K. Yasuda, A.N. Michel. Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach[J]. International Journal of Systems Science, 2001, 32(8): 1055-1061.
[28] X.M. Sun, J. Zhao, D.J. Hill. Stability and L_2 -gain analysis for switched delay systems: A delay-dependent method [J]. Automatica, 2006, 42(10): 1769-1774.
[29] R. Wang, J. Zhao. Exponential stability analysis for discrete-time switched linear systems with time-delay[J]. International Journal of Innovative Computing, Information and Control, 2007, 3(6): 1557-1564.
[30] Z.R. Xiang, W.M. Xiang. Stabilization of a class of switched nonlinear systems with average dwell time[J]. WCICA 2008. 7th World Congress on Intelligent Control and Automation, 2008, pp:1673– 1676.
[31] M. Wang, G.M. Dimirovski, J. Zhao. Robust tracking control of a class of nonlinear switched systems: An average dwell-time method[C], 2009 American Control Conference Hyatt Regency Riverfront, 2009, pp: 1983-1787.
[32] L.X. Zhang, P. Shi. l_2 - l_∞model reduction for switched LPV systems with average dwell time[J]. IEEE Transactions on Automatic Control, 2008, 53(10): 2443– 2448.
[33] D. Ma, J. Zhao. Stabilization of networked control systems via switching controllers: An average dwell time approach[J]. The Sixth World Congress on Intelligent Control and Automation, 2006, pp: 4611-4622.
[34] L. Wu, T. Qi, Z. Feng. Average dwell time approach to L_2 - L_∞control of switched delay systems via dynamic output feedback[J]. IET Control Theory and Applications, 2009, 3(10): 1425– 1436.
[35] D.W. Ding, G.H. Yang. H_∞static output feedback control for discrete-time switched linear systems with average dwell time[J]. IET Control Theory and Applications, 2010, 4(3): 381– 390.
[36] M.A. Wicks, P. Peleties, A. DeClarlo. Switched controller synthesis for the quadratic stabilization of q pair of unstable linear systems[J]. European Journal of Control, 1998, 4: 140-147.
[37] M.A. Wicks, P. Peleties, A. DeClarlo. Construction of piecewise Lyapunov function for stabilizing switched systems[C]. Process 33th Conf. Decision And Control , 1994, pp: 3492-3497.
[38] E. Feron. Quadratic stabilizability of switched systems via state and output feedback[C]. Technical report CICS-P-468, MIT, 1996, submitted to SIAM J.control .Optimization.
[39] Z. Sun. Analysis and synthesis of switched linear control systems[J]. IEEE Transactions on Automatic Control, 2004, 49(7): 1133-1137.
[40] X. Xu, P.J. Antsaklis. Stabilizability of second-order LTI switched systems[J]. International Journal of Control, 2000, 73(14): 1261-1279.
[41] Z.J. Ji. Number of switchings and design of switching sequences for controllability of switched linear systems[C]. Chinese Control Conference , 2006, pp: 1049-1054.
[42] Z.J. Ji, L. Wang, X.X. Guo. Design of switched sequences of controllability realization of switched linear systems[J]. Automica, 2007, 43(4): 662-668.
[43] L.X. Zhang, C.H. Wang, L.J. Chen. Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties[J]. IEEE Transactions on Industrial Electronics, 2009, 56(9): 3684-3692.
[44] J.C. Geromal, G.S. Deaecto. Switched state feedback control for continuous time uncertain systems[J]. Automatic, 2009, 45(2): 593-597.
[45] W. Zhang, Alessandro Abate, Jianghai Hu, Michael P. Vitus. Exponential stabilization of discrete-time switched linear systems[J]. Automatica, 2009, 45(11): 2526-2536.
[46] R. Li, Z.G. Feng, K.L. Teo, G.R. Duan. Optimal piecewise state feedback control for impulsive switched systems[J]. Mathmatical And Computer Modelling, 2008, 48(3-4): 468-479.
[47] H. Lin, P.J. Antsaklis. Stability and stabilizability of switched linear systems: A short survey of recent results[C]. Proceedings of the 2005 IEEE international symposium on intelligent control limassol, Cyprus, 2009, pp: 24-29.
[48] Z.D. Sun, S.S. Ge. Analysis and synthesis of switched linear control systems[J]. Automatica, 2005, 41(2): 181-195.
[49]吴敏,何勇.时滞系统鲁棒控制——自由权矩阵方法[M].北京:科学出版社,2008:1-2.
[50] Y.S. Moon, P. Park, P. Kwon, W.H. kwon, Y.S. Lee. Delay-dependent robust stabilization of uncertain state delayed systems[J], International Journal of Control, 2001, 74(14): 1447-1455.
[51] M. Wang, Y. He, J.H. She, G.P. Liu. Delay-dependent criteria for robust stability of time-varying delay systems[J]. Automatica, 2004, 40(8): 1435-1439.
[52] Y. He, Q.G. Wang, L. Xie, C. Lin. Further improvement of free-weighting matrices technique for systems with time-varying delay[J]. IEEE Transactions on Automatic Control, 2007, 52(2): 647-650.
[53] Q.X. Chen, L. Yu, W.A. Zhang. Delay-dependent output feedback guaranteed cost control for uncertain discrete-time systems with multiple time-varying delays[J]. IET Control Theory Application, 2007, 1(1): 97-103.
[54] D. Wang, W. Wang, P. Shi. Delay-dependent exponential stability for switched delay systems[J]. Optimal Control Application and Methods, 2009, 30(4): 383-397.
[55]M.S. Mahmoud, F.M. Al-Sunni, Y. Shi. Switched discrete-time delay systems: Delay-dependent analysis and synthsis[J]. Circuits Syst Signal Process, 2009, 28(5): 735-761.
[56] L.E. Ghaoui, F. Oustry, M. AiRami. A Cone complementarity linearization algorithm for staticoutput-feedback and related problems[J]. IEEE Transactions on Automatic Control, 1997, 42(8): 1171-1176.
[57]俞立.鲁棒控制——线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002: 1-19.
[58] L. Xie, M. Fu, C.D. Souza. H∞control and quadratic stabilization of systems with parameter uncertainty via output feedback[J]. IEEE Transactions on Automatic Control, 1992, 37(8): 1253-1256.
[1] D. Liberzon, A.S. Morse. Basic problems in stability and design of switched systems[J]. IEEE Control Systems Magazine, 1999, 19(5): 59-70.
[2] K.S. Narendra, J. Balakrishnan. A common Lyapunov function for stable LTI systems with commuting A-matrices[J]. IEEE Transactions on Automatic Control, 1994, 39(12): 2469-2471.
[3] R. Shorten, K. Narendra. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for two stable second order linear time-invariant systems[C]. Proceedings of the 1999 American Control Conference, 1999, pp. 1410-1414.
[4] R. Shorten, K. Narendra. Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable LTI systems[J]. International Journal of Control of Adaptive Control and Signal Processing, 2002, 16(10): 709-728.
[5] C. King, R. Shorten. A singularity test for the existence of common quadratic Lyapunov functions for pairs of stable LTI systems[C]. Proceedings of the 2004 American ControlConference, 2004, pp. 3881-3884.
[6] W. Dayawansa, C.F. Martin. A converse Lyapunov theorem for a class of dynamical systems with undergo switching[J]. IEEE Transactions on Automatic Control, 1999, 44(4): 751-760.
[7] J.L. Mancilla-Aguilar, R. A. Garcia. A converse Lyapunov theorem for nonlinear switched systems[J]. Systems & Control Letters, 2000, 41(1): 67-71.
[8] J. Daafouz, P. Riedinger, C. Iung. Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach[J]. IEEE Transactions on Automatic Control, 2002, 47(11): 1883-1887.
[9] L. Zhang, P. Shi, E.K. Boukas. H_∞output-feedback control for switched linear discrete-time systems with time-varying delays[J]. International Journal of Control, 2007, 80(8): 1354-1365.
[10] L.X. Zhang, C.H. Wang, L.J. Chen. Stability and stabilization of a class of multimode Linear discrete-time systems with polytopic uncertainties[J]. IEEE Transactions on Automatic Control, 2009, 56(9): 3684-3692.
[11] L.X. Zhang, P. Shi, E.K. Boukas, C. Wang. Robust l_2-l_∞filtering for switched linear discrete time-delay systems with polytypic uncertainties[J]. IET Control Theory & Applications, 2007, 1(3): 722-730.
[12] M.S. Mahmoud. Delay-dependent H_∞filtering of a class of switched discrete-time state delay systems[J]. Signal Processing, 2008, 88(11): 2709-2719.
[13] D.S. Du, B. Jiang, P. Shi, S.S. Zhou. H_∞filtering of discrete-time switched systems with state delays via switched Lyapunov function approach[J]. IEEE Transactions on Automatic Control, 2006, 52(8): 1520-1525.
[14] D.S. Du, B. Jiang, P. Shi, S.S. Zhou. Robust l_2-l_∞control for uncertain discrete-time switched systems with delays[J]. Circuits Systems Signal Processing, 2006, 25(6): 729-744.
[15] M.S. Mahmoud, P. Shi, A.W.A. Saif. Stabilization of linear switched delay systems: H 2and H_∞methods[J]. Journal of Optimization Theory and Applications, 2009, 142(3): 583-601.
[16] X.W. Liu. Stability analysis of switched positive systems: A switched linear copositive Lyapunov function method [J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2009, 56(5): 414-418.
[17] Y. Wang, W. Wang, D. Wang. LMI approach to design fault detection filter for discrete-Time switched systems with state delays[J]. International Journal ofInnovative Computing, Information and Control, 2010, 6(1): 387-397.
[18] A. Morse. Supervisory control of families of linear set-point controllers part I: Exact matching[J]. IEEE Transactions on Automatic Control, 1996, 41(10): 1413-1431.
[19] P. Peleties, R.A. DeCarlo. Asymptotic stability of m-switched systems using Lyapunov-like functions[C]. Proceedings of the 1991 American Control Conference, 1991, pp. 1679-1684.
[20] M.S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid system[J]. IEEE Transactions on Automatic Control, 1998, 43(4): 475-482.
[21] M.S. Branicky. Stability of switched and hybrid systems[C]. IEEE conference on decision and control, 1997, pp: 120-125.
[22] L. Hou, A.N. Michel, H. Ye. Stability analysis of switched systems[C]. Proc.35rd conf. Decision and control, 1996, pp: 1208-1212.
[23] S. Pettersson, B. Lennartson. Stability and robustness for hybirdsystems[C]. Proc.35rd conf. Decision and control, 1996, pp: 1202-1207.
[24] H. Ye, A.N. Michel, L. Hou. Stability theory for hybrid dynamical systems[J]. IEEE Transactions on Automatic Control, 1998, 43(4): 461-474.
[25] J.P. Hespanha, A.S. Morse. Stability of switched systems with average dwell-Time[C]. Proc.38rd conf. Decision and control, 1999, pp: 1202-1207.
[26] G.S. Zhai, B. Hu, K. Yasuda, Anthony N. Michel. Piecewise Lyapunov functions for switched systems with average dwell Time[J]. Asian Journal of Control, 2001, 2(3): 192-197.
[27] G.S. Zhai, B. Hu, K. Yasuda, A.N. Michel. Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach[J]. International Journal of Systems Science, 2001, 32(8): 1055-1061.
[28] X.M. Sun, J. Zhao, D.J. Hill. Stability and L_2 -gain analysis for switched delay systems: A delay-dependent method [J]. Automatica, 2006, 42(10): 1769-1774.
[29] R. Wang, J. Zhao. Exponential stability analysis for discrete-time switched linear systems with time-delay[J]. International Journal of Innovative Computing, Information and Control, 2007, 3(6): 1557-1564.
[30] Z.R. Xiang, W.M. Xiang. Stabilization of a class of switched nonlinear systems with average dwell time[J]. WCICA 2008. 7th World Congress on Intelligent Control and Automation, 2008, pp:1673– 1676.
[31] M. Wang, G.M. Dimirovski, J. Zhao. Robust tracking control of a class of nonlinear switched systems: An average dwell-time method[C], 2009 American ControlConference Hyatt Regency Riverfront, 2009, pp: 1983-1787.
[32] L.X. Zhang, P. Shi. l_2 - l_∞model reduction for switched LPV systems with average dwell time[J]. IEEE Transactions on Automatic Control, 2008, 53(10): 2443– 2448.
[33] D. Ma, J. Zhao. Stabilization of networked control systems via switching controllers: An average dwell time approach[J]. The Sixth World Congress on Intelligent Control and Automation, 2006, pp: 4611-4622.
[34] L. Wu, T. Qi, Z. Feng. Average dwell time approach to L_2 - L_∞control of switched delay systems via dynamic output feedback[J]. IET Control Theory and Applications, 2009, 3(10): 1425– 1436.
[35] D.W. Ding, G.H. Yang. H_∞static output feedback control for discrete-time switched linear systems with average dwell time[J]. IET Control Theory and Applications, 2010, 4(3): 381– 390.
[36] M.A. Wicks, P. Peleties, A. DeClarlo. Switched controller synthesis for the quadratic stabilization of q pair of unstable linear systems[J]. European Journal of Control, 1998, 4: 140-147.
[37] M.A. Wicks, P. Peleties, A. DeClarlo. Construction of piecewise Lyapunov function for stabilizing switched systems[C]. Process 33th Conf. Decision And Control , 1994, pp: 3492-3497.
[38] E. Feron. Quadratic stabilizability of switched systems via state and output feedback[C]. Technical report CICS-P-468, MIT, 1996, submitted to SIAM J.control .Optimization.
[39] Z. Sun. Analysis and synthesis of switched linear control systems[J]. IEEE Transactions on Automatic Control, 2004, 49(7): 1133-1137.
[40] X. Xu, P.J. Antsaklis. Stabilizability of second-order LTI switched systems[J]. International Journal of Control, 2000, 73(14): 1261-1279.
[41] Z.J. Ji. Number of switchings and design of switching sequences for controllability of switched linear systems[C]. Chinese Control Conference , 2006, pp: 1049-1054.
[42] Z.J. Ji, L. Wang, X.X. Guo. Design of switched sequences of controllability realization of switched linear systems[J]. Automica, 2007, 43(4): 662-668.
[43] L.X. Zhang, C.H. Wang, L.J. Chen. Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties[J]. IEEE Transactions on Industrial Electronics, 2009, 56(9): 3684-3692.
[44] J.C. Geromal, G.S. Deaecto. Switched state feedback control for continuous time uncertain systems[J]. Automatic, 2009, 45(2): 593-597.
[45] W. Zhang, Alessandro Abate, Jianghai Hu, Michael P. Vitus. Exponential stabilization of discrete-time switched linear systems[J]. Automatica, 2009, 45(11): 2526-2536.
[46] R. Li, Z.G. Feng, K.L. Teo, G.R. Duan. Optimal piecewise state feedback control for impulsive switched systems[J]. Mathmatical And Computer Modelling, 2008, 48(3-4): 468-479.
[47] H. Lin, P.J. Antsaklis. Stability and stabilizability of switched linear systems: A short survey of recent results[C]. Proceedings of the 2005 IEEE international symposium on intelligent control limassol, Cyprus, 2009, pp: 24-29.
[48] Z.D. Sun, S.S. Ge. Analysis and synthesis of switched linear control systems[J]. Automatica, 2005, 41(2): 181-195.
[49]吴敏,何勇.时滞系统鲁棒控制——自由权矩阵方法[M].北京:科学出版社,2008:1-2.
[50] Y.S. Moon, P. Park, P. Kwon, W.H. kwon, Y.S. Lee. Delay-dependent robust stabilization of uncertain state delayed systems[J], International Journal of Control, 2001, 74(14): 1447-1455.
[51] M. Wang, Y. He, J.H. She, G.P. Liu. Delay-dependent criteria for robust stability of time-varying delay systems[J]. Automatica, 2004, 40(8): 1435-1439.
[52] Y. He, Q.G. Wang, L. Xie, C. Lin. Further improvement of free-weighting matrices technique for systems with time-varying delay[J]. IEEE Transactions on Automatic Control, 2007, 52(2): 647-650.
[53] Q.X. Chen, L. Yu, W.A. Zhang. Delay-dependent output feedback guaranteed cost control for uncertain discrete-time systems with multiple time-varying delays[J]. IET Control Theory Application, 2007, 1(1): 97-103.
[54] D. Wang, W. Wang, P. Shi. Delay-dependent exponential stability for switched delay systems[J]. Optimal Control Application and Methods, 2009, 30(4): 383-397.
[55]M.S. Mahmoud, F.M. Al-Sunni, Y. Shi. Switched discrete-time delay systems: Delay-dependent analysis and synthsis[J]. Circuits Syst Signal Process, 2009, 28(5): 735-761.
[56] L.E. Ghaoui, F. Oustry, M. AiRami. A Cone complementarity linearization algorithm for static output-feedback and related problems[J]. IEEE Transactions on Automatic Control, 1997, 42(8): 1171-1176.
[57]俞立.鲁棒控制——线性矩阵不等式处理方法[M].北京:清华大学出版社, 2002: 1-19.
[58] L. Xie, M. Fu, C.D. Souza. H∞control and quadratic stabilization of systems withparameter uncertainty via output feedback[J]. IEEE Transactions on Automatic Control, 1992, 37(8): 1253-1256.