灰色随机时滞系统的鲁棒稳定性研究
|
摘要
本文利用Lyapuonv函数、Lyapunov-Krasovskii泛函和模型变换等方法,结合Ito ?公式、矩阵不等式、Ho lder不等式、Schur补等数学工具及灰矩阵的连续矩阵覆盖的分解技术,深入研究了灰色随机时滞系统鲁棒稳定性问题,特别是对分布型、中立型和中立---分布型灰色随机时滞系统的指数鲁棒稳定性问题,作了更为深入细致的研究,建立了一些有效的判据,获得了若干有意义的成果。
1.概述了灰色不确定随机时滞系统鲁棒稳定性的研究背景、意义和价值,综述了不确定时滞系统鲁棒稳定性的发展和研究现状,指出了灰色不确定时滞系统和不确定时滞系统在鲁棒稳定性研究方面的异同点及目前应研究和注意的问题。
2.研究了灰色随机线性时滞系统的鲁棒稳定性问题。基于本文所提供的随机微分时滞方程渐近稳定性的引理和灰矩阵的连续矩阵覆盖的分解技术,分析了灰色随机线性时滞系统鲁棒渐近稳定性,给出了时滞无关的代数判据及其自由参数的选取方法。分别利用Lyapunov函数法和模型变换法研究了该系统的p-阶矩指数鲁棒稳定性,得到了p-阶矩指数鲁棒稳定性的代数判据。通过数值例子说明了所得结果的方便性和有效性。
3.考虑了一类带有一个分布时滞项的灰色随机时滞系统。基于Lyapunov- Krasovskii泛函法探讨了这类系统的随机鲁棒稳定性和均方指数鲁棒稳定性,给出了该系统的随机鲁棒稳定性和均方指数鲁棒稳定性的时滞依赖的LMI判据,分别利用Lyapunov-Krasovskii函数法和模型变换法研究了该系统的p-阶矩指数鲁棒稳定性,获得了该系统的p-阶矩指数鲁棒稳定性的时滞依赖的代数判据。实例表明所得结果是有效的。
4.考虑了一类在确定部分和随机部分中均含一个分布时滞项的灰色随机控制系统。利用Lyapunov-Krasovskii泛函法,探讨了该类系统在一个状态反馈控制律下其闭环系统的随机鲁棒稳定性和指数鲁棒稳定性,得到了该闭环系统随机鲁棒稳定性和指数鲁棒稳定性的非线性矩阵判据和LMI判据;分别使用Lyapunov-Krasovskii泛函法和模型变换法,研究了该类系统在控制输入向量的参数矩阵为零且状态时滞各不相同时的p-阶矩指数鲁棒稳定性,提供了p-阶矩指数鲁棒稳定性的两个时滞依赖的代数判据。验证了所得判据的有效性。
5.研究了中立型灰色随机时滞系统鲁棒稳定性问题。首先,基于Lyapunov-Krasovskii泛函法,探讨了中立型灰色随机时滞系统的均方指数鲁棒稳定性问题,得到了该系统均方指数鲁棒稳定性的时滞独立性判据,进而给出了该系统几乎必然指数鲁棒稳定性的充分条件;随后,分别利用Lyapunov-Krasovskii泛函法和一个模型变换法并结合几个代数不等式,研究了中立型灰色随机时滞系统的p-阶矩指数鲁棒稳定性问题,建立了该系统p-阶矩指数鲁棒稳定性的两个时滞依赖的充分条件;最后,通过数值例子分别验证了所得判据的有效性,并比较了这些判据的保守性和实用性。
6.研究了中立---分布型灰色随机时滞系统的均方指数鲁棒稳定性问题。基于Lyapunov- Krasovskii泛函、Ito ?公式、Ho lder不等式和Schur补矩阵不等式定理,获得了中立---分布型灰色随机时滞系统的统均方指数鲁棒稳定性的时滞依赖的非线性矩阵不等式判据和线性矩阵不等式判据。验证了这些判据的有效性和实用性,并比较了判据的保守性。
7.研究了一类具有脉冲作用的灰色随机时滞系统鲁棒稳定性问题。利用本文提出的一个判定确定的脉冲随机线性时滞系统随机稳定性的引理,得出了该系统随机鲁棒稳定性的LMI判据;基于Lyapunov函数法,建立了该类系统p-阶矩鲁棒稳定性的时滞无关的代数判据。验证了所得判据的有效性。
This paper investigates the robust stability of grey stochastic time-delay systems by applying the methods of Lyapunov function, Lyapunov-Krasovskii functional and transformation model and employing the tools of Ito ? formula, matrix inequalities, Ho lder inequality and Schur complement and using the decomposition technique of the continuous matrix-covered sets of grey matrix, Especially, the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type are deeply studied. Some efficiency criteria are established. Significant results are obtained.
1. The investigated background, significance and value for grey uncertain stochastic time-delay systems are illustrated. The development history and research status of robust stability of uncertain time-delay systems are reviewed. The differences and similarities are pointed out on the study methods of robust stability between grey uncertain time-delay systems and uncertain time-delay systems, and the problems what need to be investigated and focused are proposed.
2. The problem of robust stability of grey stochastic linear time-delay systems is investigated. Firstly, based on the presented lemma of asymptotic stability for stochastic linear time-delay systems and the decomposition technique of the continuous matrix-covered sets of grey matrix, the robust asymptotic stability of grey stochastic linear time-delay systems is analyzed, and the delay- independent algebraic criteria of robust asymptotic stability are given. The method is presented to select the free parameters in the delay-independent algebraic criteria. Secondly, the p-moment exponential robust stability of grey stochastic linear time-delay systems is investigated by applying the Lyapunov function method and the transformation model method respectively. The algebraic criteria for p-moment exponential robust stability are obtained. Finally, numerical examples show the convenience and effectiveness of the criteria got in this paper.
3. A class of grey stochastic time-delay systems with a distributed-delay term is considered. Firstly, based on the Lyapunov- Krasovskii functional method, the stochastic robust stability and the exponential robust stability in mean square for grey stochastic time-delay systems with a distributed-delay term is explored. The delay-dependent criteria of stochastic robust stability are shown. Secondly, the p-moment exponential robust stability of the described system is investigated by the Lyapunov function and the transformation model respectively. The delay- dependent algebraic criteria for p-moment exponential robust stability are obtained. Finally, the examples indicate the effectiveness of the obtained criteria.
4. A class of grey stochastic control systems in which the deterministic portion and the stochastic portion have a distributed-delay term respectively is considered. The stochastic robust stability and the exponential robust stability of the close-loop systems under a state feedback control law are probed by the Lyapunov-Krasovskii functional method. The conditions for the stochastic robust stability and the exponential robust stability are derived in the forms of a nonlinear matrix inequality and a linear matrix inequality. When the parametric matrix of control input vector is a zero matrix and the time tags of states are mutual difference, the p-moment exponential robust stability of the described systems are studied by using the Lyapunov-Krasovskii functional method and the transformation model method respectively. Two delay- dependent algebraic criteria are presented. The effectiveness of the proposed criteria is verified.
5. The problem of robust stability of grey neutral stochastic time-delay systems is investigated. Firstly, based on the Lyapunov-Krasovskii functional method, the exponential robust stability in mean square for grey neutral stochastic time-delay systems is probed. The delay-independent criteria of stochastic robust stability are shown, and then a sufficient condition for almost sure exponential robust stability is proposed. Secondly, by applied the Lyapunov function and the transformation model respectively, and used several algebraic inequalities, the p-moment exponential robust stability of the described system is investigated. The delay-dependent algebraic criteria for p-moment exponential robust stability are established. Finally, Numerical examples indicate the effectiveness of the presented criteria. The conservation and practicality of these criteria are compared.
6. The problem of robust stability of grey neutral stochastic time-delay systems with distributed- delays is studied. Based on the Lyapunov-Krasovskii functional, Ito ? formula, Ho lder inequality and Schur complement theorem, the criteria of exponential robust stability in mean square for two classes of grey neutral stochastic time-delay systems with distributed-delays are derived in the forms of a nonlinear matrix inequality and a linear matrix inequality. The effectiveness and practicality of the obtained criteria are verified. The conservation of these criteria is compared.
7. The problem of robust stability of grey stochastic time-delay systems with impulsive effect is studied. By using the proposed lemma of stochastic stability of stochastic time-delay systems with impulsive effect, the criterion of stochastic robust stability for grey stochastic time-delay systems with impulsive effect is obtained. Based on the Lyapunov-Krasovskii functional method, the delay-independent algebraic condition of p-moment robust stability is established. Numerical example shows the effectiveness of the criteria derived in this paper.
1.概述了灰色不确定随机时滞系统鲁棒稳定性的研究背景、意义和价值,综述了不确定时滞系统鲁棒稳定性的发展和研究现状,指出了灰色不确定时滞系统和不确定时滞系统在鲁棒稳定性研究方面的异同点及目前应研究和注意的问题。
2.研究了灰色随机线性时滞系统的鲁棒稳定性问题。基于本文所提供的随机微分时滞方程渐近稳定性的引理和灰矩阵的连续矩阵覆盖的分解技术,分析了灰色随机线性时滞系统鲁棒渐近稳定性,给出了时滞无关的代数判据及其自由参数的选取方法。分别利用Lyapunov函数法和模型变换法研究了该系统的p-阶矩指数鲁棒稳定性,得到了p-阶矩指数鲁棒稳定性的代数判据。通过数值例子说明了所得结果的方便性和有效性。
3.考虑了一类带有一个分布时滞项的灰色随机时滞系统。基于Lyapunov- Krasovskii泛函法探讨了这类系统的随机鲁棒稳定性和均方指数鲁棒稳定性,给出了该系统的随机鲁棒稳定性和均方指数鲁棒稳定性的时滞依赖的LMI判据,分别利用Lyapunov-Krasovskii函数法和模型变换法研究了该系统的p-阶矩指数鲁棒稳定性,获得了该系统的p-阶矩指数鲁棒稳定性的时滞依赖的代数判据。实例表明所得结果是有效的。
4.考虑了一类在确定部分和随机部分中均含一个分布时滞项的灰色随机控制系统。利用Lyapunov-Krasovskii泛函法,探讨了该类系统在一个状态反馈控制律下其闭环系统的随机鲁棒稳定性和指数鲁棒稳定性,得到了该闭环系统随机鲁棒稳定性和指数鲁棒稳定性的非线性矩阵判据和LMI判据;分别使用Lyapunov-Krasovskii泛函法和模型变换法,研究了该类系统在控制输入向量的参数矩阵为零且状态时滞各不相同时的p-阶矩指数鲁棒稳定性,提供了p-阶矩指数鲁棒稳定性的两个时滞依赖的代数判据。验证了所得判据的有效性。
5.研究了中立型灰色随机时滞系统鲁棒稳定性问题。首先,基于Lyapunov-Krasovskii泛函法,探讨了中立型灰色随机时滞系统的均方指数鲁棒稳定性问题,得到了该系统均方指数鲁棒稳定性的时滞独立性判据,进而给出了该系统几乎必然指数鲁棒稳定性的充分条件;随后,分别利用Lyapunov-Krasovskii泛函法和一个模型变换法并结合几个代数不等式,研究了中立型灰色随机时滞系统的p-阶矩指数鲁棒稳定性问题,建立了该系统p-阶矩指数鲁棒稳定性的两个时滞依赖的充分条件;最后,通过数值例子分别验证了所得判据的有效性,并比较了这些判据的保守性和实用性。
6.研究了中立---分布型灰色随机时滞系统的均方指数鲁棒稳定性问题。基于Lyapunov- Krasovskii泛函、Ito ?公式、Ho lder不等式和Schur补矩阵不等式定理,获得了中立---分布型灰色随机时滞系统的统均方指数鲁棒稳定性的时滞依赖的非线性矩阵不等式判据和线性矩阵不等式判据。验证了这些判据的有效性和实用性,并比较了判据的保守性。
7.研究了一类具有脉冲作用的灰色随机时滞系统鲁棒稳定性问题。利用本文提出的一个判定确定的脉冲随机线性时滞系统随机稳定性的引理,得出了该系统随机鲁棒稳定性的LMI判据;基于Lyapunov函数法,建立了该类系统p-阶矩鲁棒稳定性的时滞无关的代数判据。验证了所得判据的有效性。
This paper investigates the robust stability of grey stochastic time-delay systems by applying the methods of Lyapunov function, Lyapunov-Krasovskii functional and transformation model and employing the tools of Ito ? formula, matrix inequalities, Ho lder inequality and Schur complement and using the decomposition technique of the continuous matrix-covered sets of grey matrix, Especially, the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type are deeply studied. Some efficiency criteria are established. Significant results are obtained.
1. The investigated background, significance and value for grey uncertain stochastic time-delay systems are illustrated. The development history and research status of robust stability of uncertain time-delay systems are reviewed. The differences and similarities are pointed out on the study methods of robust stability between grey uncertain time-delay systems and uncertain time-delay systems, and the problems what need to be investigated and focused are proposed.
2. The problem of robust stability of grey stochastic linear time-delay systems is investigated. Firstly, based on the presented lemma of asymptotic stability for stochastic linear time-delay systems and the decomposition technique of the continuous matrix-covered sets of grey matrix, the robust asymptotic stability of grey stochastic linear time-delay systems is analyzed, and the delay- independent algebraic criteria of robust asymptotic stability are given. The method is presented to select the free parameters in the delay-independent algebraic criteria. Secondly, the p-moment exponential robust stability of grey stochastic linear time-delay systems is investigated by applying the Lyapunov function method and the transformation model method respectively. The algebraic criteria for p-moment exponential robust stability are obtained. Finally, numerical examples show the convenience and effectiveness of the criteria got in this paper.
3. A class of grey stochastic time-delay systems with a distributed-delay term is considered. Firstly, based on the Lyapunov- Krasovskii functional method, the stochastic robust stability and the exponential robust stability in mean square for grey stochastic time-delay systems with a distributed-delay term is explored. The delay-dependent criteria of stochastic robust stability are shown. Secondly, the p-moment exponential robust stability of the described system is investigated by the Lyapunov function and the transformation model respectively. The delay- dependent algebraic criteria for p-moment exponential robust stability are obtained. Finally, the examples indicate the effectiveness of the obtained criteria.
4. A class of grey stochastic control systems in which the deterministic portion and the stochastic portion have a distributed-delay term respectively is considered. The stochastic robust stability and the exponential robust stability of the close-loop systems under a state feedback control law are probed by the Lyapunov-Krasovskii functional method. The conditions for the stochastic robust stability and the exponential robust stability are derived in the forms of a nonlinear matrix inequality and a linear matrix inequality. When the parametric matrix of control input vector is a zero matrix and the time tags of states are mutual difference, the p-moment exponential robust stability of the described systems are studied by using the Lyapunov-Krasovskii functional method and the transformation model method respectively. Two delay- dependent algebraic criteria are presented. The effectiveness of the proposed criteria is verified.
5. The problem of robust stability of grey neutral stochastic time-delay systems is investigated. Firstly, based on the Lyapunov-Krasovskii functional method, the exponential robust stability in mean square for grey neutral stochastic time-delay systems is probed. The delay-independent criteria of stochastic robust stability are shown, and then a sufficient condition for almost sure exponential robust stability is proposed. Secondly, by applied the Lyapunov function and the transformation model respectively, and used several algebraic inequalities, the p-moment exponential robust stability of the described system is investigated. The delay-dependent algebraic criteria for p-moment exponential robust stability are established. Finally, Numerical examples indicate the effectiveness of the presented criteria. The conservation and practicality of these criteria are compared.
6. The problem of robust stability of grey neutral stochastic time-delay systems with distributed- delays is studied. Based on the Lyapunov-Krasovskii functional, Ito ? formula, Ho lder inequality and Schur complement theorem, the criteria of exponential robust stability in mean square for two classes of grey neutral stochastic time-delay systems with distributed-delays are derived in the forms of a nonlinear matrix inequality and a linear matrix inequality. The effectiveness and practicality of the obtained criteria are verified. The conservation of these criteria is compared.
7. The problem of robust stability of grey stochastic time-delay systems with impulsive effect is studied. By using the proposed lemma of stochastic stability of stochastic time-delay systems with impulsive effect, the criterion of stochastic robust stability for grey stochastic time-delay systems with impulsive effect is obtained. Based on the Lyapunov-Krasovskii functional method, the delay-independent algebraic condition of p-moment robust stability is established. Numerical example shows the effectiveness of the criteria derived in this paper.
引文
[1] R. E. Moore, Interval Analysis[M]. Prentice Hall,1966
[2] C. L. Jiang, Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems[J]. Int. J. Contr , 1988, 47(5): 1563-1565
[3] J. Chen, Sufficient conditions on stability of interval matrices: connections and new results[J]. IEEE Trans. Automa. Contr., 1992, 7(4): 541-544
[4] K.Wang, A.N.Michel,D.Liu, Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices[J]. IEEE Trans. Automat. Contr., 1994, 39(6): 1251-1255
[5] M.B.Argoun, On sufficient conditions for the stability of interval matrices[J]. Int. J. Contr., 1996, 144: 1245-1250
[6]廖晓昕,罗琦,梅正扬,关于区间矩阵确定性、可控性、可观性的充要条件的注记[J].自动化学报,1998, 24(6): 833-849
[7] I. Brewer, Sufficient conditon for robust stability of an interval matrix[J]. Pro. of the ACC[C]. 2001, 2955- 2 956
[8]廖晓昕,区间动力系统Robust稳定性进展[J].数学进展,1992, 21(2): 169-184
[9]毛维杰,禇健,孙优贤,区间系统鲁棒稳定的顶点判据[J].浙江大学学报(工学版),2000, 34(1): 5-8
[10]吴方向,史忠科,戴冠中,动态区间系统的鲁棒稳定性[J].控制理论与应用,2001, 18(1): 113-115
[11]高利新,汪治华,区间动力系统的鲁棒稳定性分析[J].应用数学,2004,17(4): 497-502
[12] E. Jen Definitions [ EB/ OL ]. Santa Fe Institute Robustness Site , RS-2001-009 , http:/ / discuss. santafe. edu/robustness, 2001, Oct., 22th.
[13]接婧,国际学术界对鲁棒性的研究[J].系统工程学报,2005, 20(2): 153-159
[14] M. Malek-Zavarei and M.Jamshidi, Time-Delay Systems Analysis, Optimization and Applica- tion[M]. Amsterdam, North-Holland, 1987
[15] J.K .Hale, S .M. Verduyn Lunel, Introduction to Functional Differential Equations (Applied Mathematical Sciences, Vol.99 )[M]. New York: Springer-Verlag, 1993
[16] S. Boyd, L.E. Ghaoui, E. Feron, et al. Linear matrix inequality in system and control theory[J]. S IAM Studies in Applied Mathematics, Philadelphia: SIAM, 1994
[17] S.S. Wang, B.S. Chen, T.P. Lin, Robust stability of uncertain time-delay systems[J]. Int. J Contr., 1987, 46: 963-976
[18] T.J. Su, T.S. Kou, Y.Y. Sun, Robust stability for linear time-delay systems with linear parameter perturbation[J]. Int. J Systems Sci., 1988, 19: 2123-2129
[19] E. Cheres, Z.J. Palmor, S. Gutman, Quantitative measures of robustness for systems including delayed perturbations[J]。IEEE Trans. Auto. Contr., 1989, 34: 1203-1204
[20] A. Hmamed, Further results on the stability of uncertain time-delay systems[J]. Int. J. Syst. Sci., 1991, 22(3): 605-614
[21] K.K. Shyu, J.J. Yan, Robust stability of uncertain time-delay systems and its stablization by variable construction control[J]. Int. J. Control, 1993, 57(1): 237-246
[22] H. Trinh and M. Aldeen, On the stability of linear systems with delayed perturbations[J]. IEEE Trans. Automat. Contr., 1994, AC-39(9): 1948-1951
[23] H. Trinh and M. Aldeen, Stability robustness bounds for linear systems with delayed perturbations[J]. IEEE Proc. Pt. D., 1995, 142(4): 345-350
[24] H.G. Chen, K.W. Han, Improved quantitative measures of robustness for multivariable systems[J]. IEEE Trans. Automat. Contr., 1994, AC-39(4): 807-810
[25]俞立,陈国定,杨马英,具有滞后摄动的线性系统鲁棒稳定性分析[J].控制理论与应用,1999, 16(4): 577-579
[26] L.H. Xie, Output feedback H∞control of systems with parameter uncertainty[J]. Int. J. Control, 1996, 63(4): 741-750
[27] F.H. Hsiao, Stabilization of uncertain time-delay systems with seres nonlinearities[J]. Int. J. Systems Sci., 1993, 24: 2175-2186
[28] T.J. Su, P.L. Liu, Robust stability of delay dependence for linear uncertain systems[J]. IEEE.Trans. Auto. Contr., 1992, 37: 1656-1659
[29] T.J. Su, P.L. Liu, Robust stability for linear uncertain time-delay systems with delay- dependence[J]. Int. J. Systems Sci., 1993, 24: 1067-1080
[30] B.G. Xu, Delay-dependent stability for linear uncertain time-delay systems[J]. Control Theory and Applications, 1996,13(4):426-430
[31] Y.G. Gu, S.C.Wang etc., On delay-dependent stability and decay estimate for uncertain systems with time- varying delay[J]. Technical Communique, 1998, 34(8): 1035-1039
[32] K. G u, Discretized LMI set in the stability problem for linear uncertain time-delay systems[J].Int. J. Control, 1997, 68(4): 923-934
[33] K. G u , A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems[J]. In t. J. Robust & Nonlinear Control, 1999, 9(1):1-4
[34] K. Gu, A further refinement of discretized Lyapunov functional method for the stability of time- delay systems[J]. Int. J. Control, 2001,74 (10): 967-976
[35] Q.L. Han, K. Gu, On robust stability of time-delay systems with norm-bounded uncertainty[J]. IEEE Trans. Automat. Contr., 2001,46(9):1426-1431
[36] E. Fridman, U. Shaked. Delay-dependent stability and H∞control: constant and time-varying delays[J]. In t. J. Control, 2003, 76(1): 4 8-60
[37] P. Park, A delay-dependent stability criterion for systems with uncertain time-invariant delays[J]. IEEE Trans. Automat. Contr., 1999, 44 (4): 876-877
[38] Y.S. Moon, P.Park, W.H. Kwon, et al. Delay-dependent robust stabilization of uncertain state- delayed systems[J]. Int. J. Control. 2001, 74 (14): 1 447-1455
[39] T.J.Su, C.G.Huang, Robust stability of delay dependence for linear uncertain systems[J]. IEEE Trans. Automa. Contr.,1992,37(10):1656-1659
[40] X. Li, C.E. de Souza, Delay-dependent robust stability and stabilization of uncertain linear delay systems: A Linear Matrix Inequality approach[J]. IEEE Trans. Automat. Contr., 1997, 42(8): 1144-1148
[41] Y.Y. Cao, Y.X. Sun, C .W. Cheng, Delay-dependent robust stabilization of uncertain systems with multiple state delays[J]. IEEE Trans. Automat. Contr., 1998, 43(11): 1608-1612
[42] P.L. Liu, T.J. Su, Robust stability of interval time-delay systems with delay dependence. Systems & Control Letters[J], 1998,33(4): 231-239
[43] Y.Y. Cao, J. Lam Computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations[J]. Int. J. Sys. Sci., 2000,31(3): 359-365
[44] J.H. Kim, Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty. IEEE Trans. Automat. Contr., 2001, 46(5): 789-792
[45] D.Yue, S. Won, An improvement on’Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty’[J]. IEEE Trans. Automat. Contr., 2002, 47(2): 407-408
[46] Y. Xia, Y. Jia, Robust stability functionals of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functions[J]. Int. J. Control, 2002, 75(16):1427-1434
[47] Y. Xia, Y. Jia, Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals[J]. Systems & Control Letters, 2003, 50(3): 183 -193
[48] D.Yue, Robust stabilization of uncertain systems with unknown input delay[J]. Automatica, 2004, 40(2): 331- 336
[49] L.L. Xiong, S.M. Zhong, J.K. Tian, Novel robust stability Criteria of uncertain neutral systems with discrete and distributed delays[J]. Chaos Solitons & Fractals, 2007, Available online at www.sciencedirect.com
[50] K. Gu, S.I. Niculescu, Additional dynamics in transformed time delay systems[J]. IEEE Trans. Automat. Contr., 2000, 45(3): 572-575
[51] K. Gu, S.I. Niculescu, Further remarks on additional dynamics in various model transformations of linear delay systems[J]. IEEE Trans. Automat. Contr., 2001, 46(3): 497-500
[52] E. Fridman, New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems[J]. Systems & Control Letters, 2001, 43(4): 309-319
[53] E. Fridman, U. Shaked, New bounded real lemma representations for time-delay systems and their applications [J]. IEEE Trans. Automat. Contr., 2001, 46 (12): 1973-1979
[54] E. Fridman, U. Shaked, An improved stabilization method for linear time-delay systems[J]. IEEE Trans. Automat. Contr., 2002, 47(11): 1931-1937
[55] E. Fridman, Stability of linear descriptor systems with delay: a Lyapunov-based approach[J]. J. Math. Anal. Appl., 2002, 273(1): 24-44
[56] E. Fridman, U. Shaked, On delay-dependent passivity[J]. IEEE Trans. Automat. Contr., 2002, 47(4): 664-669
[57] E. Fridman, U. Shaked, Parameter dependent stability and stabilization of uncertain time-delay systems[J]. IEEE Trans. Automat. Contr.l, 2003, 48(5): 861-866
[58] Y.S. Lee, Y.S. Moon, W.H. Kwon, et al., Delay-dependent robust H∞control for uncertain systems with a state-delay[J]. Automatica, 2004, 40(1): 65-72
[59] Q.L. Han A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays[J]. Automatica, 2004, 40(10): 1791-1796
[60] Q.L. Han, Stability criteria for a class of linear neutral systems with time-varying discrete and distributed delays[J]. IMA Journal of Math. Contr. and Info., 2003, 20(4): 371- 386
[61] Q.L. Han, Robust stability of uncertain delay-differential systems of neutral type[J]. Automatica,2002, 38(4): 718-723
[62] S.I. Niculescu, On delay-dependent stability under model transformations of some neutral linear systems[J]. Int. J. Control, 2001, 74(6): 608-617
[63] S.I. Niculescu, Optimizing model transformations in delay-dependent analysis of neutral systems: A control-based approach[J]. Nonlinear Analysis, 2001, 47(8): 5378-5390
[64] C.H.Lien, Stability and stabilization criteria for a class of uncertain neutral systems with time- varying delays [J]. Journal of Optimization Theory and Applications, 2005, 124: 637- 657
[65] Q.L. Han On robust stability of neutral systems with time-varying discrete delay and norm- bounded uncertainty[J]. Automatics, 2004, 40(6): 1087-1092
[66] P.L. Liu, On the stability of neutral-type uncertain systems with multiple time delays[J]. Int. J. Appl. Math. Comput. Sci., 2005, 15(2): 221-229
[67] B. Wang, S.M. Zhang, On novel stability criterion of neutral systems with time-varying delay[J]. Appl. Math. Compt., 2007, Available online at www.sciencedirect.com
[68] W.H. Chen, W.X. Zheng, Delay-dependent robust stabilization for uncertain neutral systems with distributed delays[J]. Automatic, 2007, 43: 95-104
[69] K.W. Yu, C.H. Lie, Stability critera for uncertain neutral systems with interval time-varying delays[J]. Chaos Soltion & Fractals, 2007, Available online at www.sciencedirect.com
[70] Y. Chen, A.K. Xue, et al., On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations[J]. Nonlinear Analysis, 2007, doi:10.1016/j.na. 2007.01.070
[71] L.G. Xiong, S.M. Zhong, J.K. Tian, Novel robust stability criteria of uncertain neutral systems with discrete and distributed delays[J]. Chaos Soltion & Fractals, 2007, Available online at www.sciencedirect.com
[72]何勇,自由权矩阵的时滞相关鲁棒稳定与镇定[D].中南大学,2004
[73] Y. He, M. Wu, et al., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays[J]. Systems & Control Letters, 2004, 51: 57-65
[74] M. Wu, Y. He, J.H. She, New delay-dependent stability criteria and stabilizing method for neutral systems[J]. IEEE Trans. Automat. Contr. 2004, 49: 2266-2271
[75] BerntΦksendal, Stochastic Differential Equations, An Introduction with Applications[M]. Fourth Edition, Springer-Verlag,北京:世界图书出版公司,1998
[76] R.Z. Hasminskii, Stochastic Stability of Differential Equations[M]. Netherlands: Sijthoff andNoordhoff, 1980
[77] V.B. Kolmanovskii, V.R. Nosov, Stability of Functional Differential Equations[M]. London: Acadenic Press, 1986
[78] S.-E.A Mhammed, Stochastic Functional Differential Equations[M]. New York: Longman, 1986
[79]胡宣达,随机微分方程稳定性理论[M].南京大学出版社,1986
[80]冯昭枢,随机系统的稳定性与镇定[D].华南理工大学,1990
[81]刘永清,冯昭枢,大型动力系统的理论与应用,卷4:随机·稳定与控制[M].华南理工大学出版社,1992
[82]刘永清,邓飞其,大型动力系统的理论与应用,卷10:随机系统的变结构控制[M].华南理工大学出版社,1992
[83] V.B. Kolmanoviskii, A. Myshkis, Applied Theory of Functional Differential Equations[M]. Dordrecht: Kluwer Academic Publishers, 1992
[84] X. Mao, Exponential Stability of Stochastic Differential Equations[M], New York: Marcel Dekker, 1994
[85] E.I. Verriest, Stabilization of deterministic and stochastic systems with uncertain time delays[J]. Proceedings of the 33th IEEE Conference on Decision and control, Lake Buene Vista (FL), 1994: 3829-3833
[86] E.I. Verriest, P. Florchinger, Stability of stochastic systems with uncertain time delays[J]. Systems & Control Letters, 1995, 24:41-47
[87] E.I. Verriest, Stability and stabilization of stochastic systems with distributed delays[J]. Proceedings of the 34th IEEE Conference on Decision and control, New Orleans(LA), 1995: 2205-2209
[88]邓飞其,冯昭枢,刘永清,时不变线性Ito ?随机系统均方稳定性的充分条件[J].自动化学报,1996, 22(4): 510-512
[89] T. Sasagawa, J.L. Willems, Parametrization method for calculating exact stability bounds of stochastic linear systems with multiplicative noise[J]. Automatica, 1996, 32(12): 1741-1747
[90] X. Mao, Exponential stability in mean square of neutral stochastic functional differential equations[J]. Syst. Contr. Letters, 1995, 26: 245-251
[91] X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations[J]. SIAM Journal on Mathematical Analysis, 1997, 28(2): 389-401
[92]廖晓昕,毛学荣,随机中立型微分方程稳定性[J].科学通报,1997, 42(10): 1117-1118
[93] X. Mao, Stochastic Differential Equations and Their Applications[M], Horwood Publlshing Limited, 1997
[94] X.X. Liao, X. Mao, Almost sure exponential stability of neutral stochastic differential equat- ions[J]. J. Math. Anal. & Appal. 1997, 212: 554-570
[95]沈轶,廖晓昕,随机中立型泛函微分方程指数稳定的Razumikhin型定理[J].科学通报,1998, 43(21): 2272-2275
[96] X. Mao, LaSalle-type theorems for stochastic differential delay equations[J]. J. Math. Anal. Appl., 1999, 236: 350-369
[97] K.Liu, X. Xia, On the exponential stability in mean square of neutral stochastic functional differential equations[J]. Systems & Control Letters, 1999, 37(4):207-215.
[98] P. Florchinger, Stability of some linear stochastic systems with distributed delays[J]. Proceedings of the 40th IEEE Conference on Decision and control, Orlando, Florida USA, 2001: 4744-4745
[99] X. Mao, A note on the LaSalle-type theorems for stochastic differential delay equations[J]. J. Math. Anal. Appl., 2002, 268: 125-142
[100] A.F. Ivanov, Y.I. Kazmerchuk, A.V. Swishchuk, Theory, stochastic stability and applications of stochastic delay differential equations: a survey of recent results[J]. Differential Equation and Dynamical Systems, 2003, 11:55-116
[101] E.K. Boukas, Control of stochastic systems with time-varying multiple time delays: LMI approach. Journal of Optimization Theory and Applications, 2003, 119(1): 19-36
[102]江明辉,沈轶,廖晓昕,中立型随机时滞系统的渐近稳定性[J].华中科技大学学报(自然科学版), 2005, 33(11): 71-73
[103] E.I. Verriest, Stochastic stability of a class of distributed delay systems[J], Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, 2005IEEE: 5048-5053
[104]张俊,沈轶等,中立型非线性随机时滞系统的渐近稳定性[J].华中科技大学学报(自然科学版), 2006, 34(10): 61-63
[105] W.H. Zhang, X.Z. Liu, et al., On stabilization for a class of nonlinear stochastic time-delay systems: a matrix inequality apporach[J]. Journal of Control Theory and Applications, 2006, 3:229-234
[106] Y. Shen, Q. Luo, X. Mao, The improved LaSalle-type theorems for stochastic functionaldifferential equations[J]. J. Math. Anal. Appl., 2006, 318: 134-154
[107] B. Ficak, Point delay methods applied to the investigation of stability for a class of distributed delay systems[J]. Systems & Control Letters, 2007, 56(3): 223-229
[108] J. Randjelovic, S.Jankovic,On the pth moment exponential stability criteria of neutral stochastic functional differential equations[J]. Journal of Mathematical Analysis and Applications, 2007, 326(1):266-280
[109] E.K. Boukas, H. Yang, Exponential stabilizability of stochastic systems with Markovian jumping parameters [J]. Automatica, 1999, 35: 1437-1441
[110] X. Mao, L. Shaikhet, Delay-dependent criteria for stochastic differential delay equations with Markovian switching[J]. Stochastic processes and Their Applications, 2000, 3(2): 87-101
[111] Y.Y. Cao, J. Lam, L.S. Hu, Delay-dependent stochastic stability and H∞analysis for time- delay systems with Markovian jumping parameters[J]. J. Franklin Institute, 2003, 340:423-434
[112] J.B.R. do Val, C. Nespoli, Stochastic stability for Markovian jump linear systems subject to a crucial failure event[J]. Proceeding of the American Control Conference, Denver, Colorado, 2003:4249-4254
[113] P. Bolzern, P. Colaneri, G. De Nicolao, On almost sure stability of continuous-time Markov jump linear systems[J]. Automatica, 2006, 42: 983-988
[114] X. Mao, Robustness of exponential stability of stochastic differential delay equations[J]. IEEE Trans. Auto mat. Contr., 1996, Ac-41: 442-447
[115] X. Mao, N. Koroleva, A. Rodkina, Robust stability of uncertain stochastic differential delay equations[J]. Syst. Contr. Lett., 1998, 35(5): 325-336
[116] X.X. Liao, X. Mao, Exponential stability of stochastic delay interval systems[J]. Syst. Contr. Lett., 2000, 7(2):307-328.
[117] S.L.Xie, L.H. Xie, Stabilization of a class of uncertain large-scale stochastic systems with time delay[J]. Automatica, 2000, 36: 161-167.
[118] D. Yue, S. Won, Delay dependent robust stability of stochastic systems with time delay and nonlinear uncertainies[J]. Electronics Letters, 2001, 37(15): 992-993
[119] C.Y. Lu, J.S.H. Tsai, T.J. Su, An LMI-based approach for robust stabilization of uncertain stochastic systems with times-varying delays[J]. IEEE Trans, Automat. Contr., 2003, 48(2): 286-289
[120]包俊东,时滞随机系统的鲁棒稳定性、镇定与控制[D].华南理工大学学报, 2004
[121] C.Y. Lu, T.J. Su, J.S.H. Tsai, On robust stabilization of uncertain stochastic time-delay systems—an LMI- based approach[J]. Journal of the Franklin Institute, 2005, 342: 473-487
[122] W.H. Chen, Z.H. Guan, X.M.Lu, Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach[J]. Syst.Contr.Lett., 2005, 54(6): 547-555
[123] G.L. Wei, Z.D. Wang, et al. Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances[J]. Systems & Control Letters, 2007, 56: 623-633
[124] Z.D. Wang, Y.R. Liu, et al., Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays[J], Physics Letters A, 2006, 354(4): 288-297
[125] Z.D. Wang, J.A. Fang, X.H. Liu, Global stability of stochastic high-order neural networks with discrete and distributed delays[J]. Chaos Solitons & Fractals, 2006,
[126] W.W. Su, Y.M. Chen, Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays[J]. Communications in Nonlinear Science and Numerical Simulation, 2007,
[127] S.Y. Xu, P. Shi, Y.M. Chu, et al., Robust stochastic stabilization and H∞control of uncertain neutral stochastic time-delay systems[J]. Journal of Mathematical Analysis and Applications, 2006, 314(1): 1-16
[128]江明辉,沈轶,廖晓昕,不确定中立线性随机时滞系统的鲁棒稳定性[J].应用数学和力学, 2007, 28(6):741-748
[129] E.K. Boukas, P. Shi, stochastic stability and guaranteed cost control of discrete time uncertain systems with Markovian jumping parameters[J]. Int. J. Control, 1998, 8: 1155-1156
[130] X. Mao, Robustness of stability of stochastic differential equations with Marlovian switching[J]. Stability and Control: Theory and Applications, 2000, 3(1): 48-61
[131] Z.D. Wang, H.Qiao, K.J. Burnham, On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters[J]. IEEE Trans. Automat. Contr., 2002, 47(4): 640-646
[132] J. D. Bao, F.Q. Deng, Q. Luo, Robust Stochastic, Stabilization of uncertain Markovian jumping systems with distributed time-delay based on LMI’s approach[J]. Proceedings of The International Symposium on Intelligent Control, Houston USA, 2003: 484-489
[133] Z.H. Guan, W.H. Chen, J.X. Xu, Delay-dependent stability and stabilizability of uncertain jump bilinear staochastic systems with mode-depentent time-delays[J]. Int. J. Syst. Contr. Sci., 2005, 36(5): 275-285
[134] J.L.Deng, Control Problems of Grey Systems[J]. Syst. Contr. Lett., 1982, 1(5): 288-294
[135]邓聚龙,灰色控制系统[J].华中工学院学报,1982, 10(3): 9-18
[136]刘凯,灰色集合于灰色系统的稳定性.华中工学院学报,1982, 10(3): 23-25
[137]陈绵云,灰色系统的稳定性与镇定问题[J].模糊数学,1985, 2: 101-106
[138]邓聚龙,周朝顺,灰色线性定常系统的反馈镇定及其稳定性充分判据[J].模糊数学,1985, 2: 107-110
[139] C.S.Zhou, J.L.Deng, The stability of the grey linear System[J]. Int. J. Control, 1986, 43(1): 313-320
[140]周朝顺,灰色系统稳定性判据[J].华中工学院学报,1986, 14(1): 23-26
[141]邓聚龙,周朝顺,灰色系统稳定性充分条件及其在学习时变系统稳定性分析中的应用[J].信息与控制,1987, 4: 24-27
[142]周朝顺,阙泰林,互联灰色动态系统稳定性的充分条件[J].华中理工大学学报,1989, 17(2): 83-87
[143]何灿芝,陈强,关于灰色线性时滞系统的稳定性[J].湖南大学学报,2001, 28(1): 5-7
[144]万上海,周宗福,灰色线性时滞系统的稳定性[J].安徽工程科技学院学报,2005, 20(2): 63-65
[145]周朝顺,邓聚龙,阙泰林,灰色离散系统的稳定性充分条件[J].华中理工大学学报, 1988, 16(4): 141-145
[146] C.S.Zhou, J.L.Deng, Stability analysis of grey discrete-time systems[J]. IEEE Trans. Auto. Contr., 1989, 34(2): 173-175
[147]彭晓林,罗晓,灰色离散系统稳定与不稳定的代数判据[J].应用数学,1991, 4(2): 76-81
[148]陈菊芳,非线性灰色离散系统零解的稳定性[J].应用数学学报,1995, 18(1): 123-128
[149]李建平,灰色时变离散系统的稳定性分析[J].经济数学,1996, 13(2): 92-95
[150]刘碧玉,灰色时滞离散大系统的稳定性[J].系统工程,1996, 14(3): 15-17
[151]周宗福,郑祖庥,非线性灰色时滞离散系统的稳定性[J].应用数学学报,2004, 27(2): 371-374
[152] Q.X. Li, S.F. Liu, The foundation of the grey matrix and the grey input-output analysis[J], Appl. Math. Modell., 2008, 32(3): 267-291
[153]苏春华,刘思峰,灰色随机线性时滞系统的渐近稳定性[J].控制与决策, 2008, 23(5): 571-574
[154]邓聚龙,灰理论基础[M].武汉:华中科技大学出版社,2002
[155]刘思峰,党耀国,方志耕,灰色系统理论及其应用[M].北京:科学出版社,2004
[156] V. D. Mil man, A. D. M yshkis, On the stability of motion in presence of impulses[J]. Siberian Math J., 1960: 233- 237.
[157] D.D. Bainov, P.S. Simeonov, System with impulse effect, Stability, Theory and Applications[M], New York: Wiley, 1989
[158] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations [M] . Singapore: World Scientific, 1989
[159] A.M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, Singapore: World Scientific, 1995
[160] A. V. Anokhin, On linear impulsive systems for functional differential equations[J]. Soviet Math Dokl, 1986, 33: 220-223
[161] S. I. Gurgula, Investigation of the stability of solutions of impulsive systems by Lyapunov’s second method[J]. Ukrainian Math. J. 1982, 1: 100-103
[162] Angelova J ,Dishliev A. Continuous dependence and uniform stability of solution of impulsive differential equation on impulsive moment s[J] . Nonlinear Analysis ,1997 ,28: 825-835
[163] M. U. Akhmetov, A. Zafer, Stability of the zero solution of impulsive differential equations by the Lyapunov second method[J]. Journal of Mathematical Analysis and Applications, 2000, 248: 69-82
[164] A A. Soliman, On stability of perturbed impulsive differential systems[J]. Applied Mathematics and Computation, 2002 ,133 :105～117
[165] A A. Soliman, Stability criteria of impulsive differential systems[J] . Applied Mathematics and Computation, 2003, 134: 445～457
[166] J.R. Yan, J.H. Shen, Impulsive stabilization of functional differential equations by Lyapunov–Razumikhin functions[J]. Nonlinear Analysis, 1999, 37: 245–255
[167] L.M.Stamova, G.T. Stamov, Lyapunov-Razumikhin method for impulsive differential equations and applications to the population dynamics[J]. J. Comput. Appl. Math. , 2001, 130: 163～171.
[168] X. Liu, G. Ballinger, Uniform asymptotic stability of impulsive delay differential equations[J]. Computers and Mathematics with Applications ,2001 ,41 :903～915
[169] Y.P. Xing, M.A. Han, A new approach to stability of impulsive functional differential equations[J]. Appl. Math. Comput., 2004, 151: 835–847
[170] K. Liu, X.L. Fu, Stability of functional differential equations with impulses[J]. J. Math. Anal. Appl. 2007, 328: 830–841
[171] Z. Kamont, J. Turo, B. Zubik-Kowal, Differential and difference inequalities generated by mixed problems for hyperbolic functional differential equations with impulses[J]. Appl. Math. Comput., 1996, 80: 127–154
[172] Z. Guan, Impulsive inequalities and stability of large scale singular measure differential systems with unbounded delays[J]. Dyn. Contin. Discrete Impuls. Syst. 1997, 3: 113–130
[173] X. Liu, X. Shen, Y. Zhang, A comparison principle and stability for large-scale impulsive delay differential systems[J]. Anziam J., 2005, 47: 203–235
[174] D. Xu, Z. Yang, Impulsive delay differential inequality and stability of neural networks[J]. J. Math. Anal. Appl. 2005, 305: 107–120
[175]D.Y. Xu, Z.G. Yang, Z.C. Yang, Exponential stability of nonlinear impulsive neutral differential equatons with delays [J]. Nonlinear Analysis, 2007, 67: 1426-1439
[176]侯振挺,李俊平等,随机脉冲泛函微分方程理论[J].长沙铁道学院学报,2001, 19(3): 1-5
[177] H.J. Wu, J.T. Sun, p-Moment stability of stochastic differential equations with impulsive jump and Markovian switching[J]. Autonatica, 2006, 42: 1753-1759
[178] Z.G. Yang, D.Y. Xu, L. Xiang, Exponential p-stability of impulsive stochastic differential equations with delays [J]. Physics Letters A, 2006, 359: 129-137
[179] Z.G. Yang, D.Y. Xu, Mean square exponential stability of impulsive stochastic differential equations[J]. Applied Mathematics Letters, 2007, 20: 938-945
[2] C. L. Jiang, Sufficient and necessary condition for the asymptotic stability of discrete linear interval systems[J]. Int. J. Contr , 1988, 47(5): 1563-1565
[3] J. Chen, Sufficient conditions on stability of interval matrices: connections and new results[J]. IEEE Trans. Automa. Contr., 1992, 7(4): 541-544
[4] K.Wang, A.N.Michel,D.Liu, Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices[J]. IEEE Trans. Automat. Contr., 1994, 39(6): 1251-1255
[5] M.B.Argoun, On sufficient conditions for the stability of interval matrices[J]. Int. J. Contr., 1996, 144: 1245-1250
[6]廖晓昕,罗琦,梅正扬,关于区间矩阵确定性、可控性、可观性的充要条件的注记[J].自动化学报,1998, 24(6): 833-849
[7] I. Brewer, Sufficient conditon for robust stability of an interval matrix[J]. Pro. of the ACC[C]. 2001, 2955- 2 956
[8]廖晓昕,区间动力系统Robust稳定性进展[J].数学进展,1992, 21(2): 169-184
[9]毛维杰,禇健,孙优贤,区间系统鲁棒稳定的顶点判据[J].浙江大学学报(工学版),2000, 34(1): 5-8
[10]吴方向,史忠科,戴冠中,动态区间系统的鲁棒稳定性[J].控制理论与应用,2001, 18(1): 113-115
[11]高利新,汪治华,区间动力系统的鲁棒稳定性分析[J].应用数学,2004,17(4): 497-502
[12] E. Jen Definitions [ EB/ OL ]. Santa Fe Institute Robustness Site , RS-2001-009 , http:/ / discuss. santafe. edu/robustness, 2001, Oct., 22th.
[13]接婧,国际学术界对鲁棒性的研究[J].系统工程学报,2005, 20(2): 153-159
[14] M. Malek-Zavarei and M.Jamshidi, Time-Delay Systems Analysis, Optimization and Applica- tion[M]. Amsterdam, North-Holland, 1987
[15] J.K .Hale, S .M. Verduyn Lunel, Introduction to Functional Differential Equations (Applied Mathematical Sciences, Vol.99 )[M]. New York: Springer-Verlag, 1993
[16] S. Boyd, L.E. Ghaoui, E. Feron, et al. Linear matrix inequality in system and control theory[J]. S IAM Studies in Applied Mathematics, Philadelphia: SIAM, 1994
[17] S.S. Wang, B.S. Chen, T.P. Lin, Robust stability of uncertain time-delay systems[J]. Int. J Contr., 1987, 46: 963-976
[18] T.J. Su, T.S. Kou, Y.Y. Sun, Robust stability for linear time-delay systems with linear parameter perturbation[J]. Int. J Systems Sci., 1988, 19: 2123-2129
[19] E. Cheres, Z.J. Palmor, S. Gutman, Quantitative measures of robustness for systems including delayed perturbations[J]。IEEE Trans. Auto. Contr., 1989, 34: 1203-1204
[20] A. Hmamed, Further results on the stability of uncertain time-delay systems[J]. Int. J. Syst. Sci., 1991, 22(3): 605-614
[21] K.K. Shyu, J.J. Yan, Robust stability of uncertain time-delay systems and its stablization by variable construction control[J]. Int. J. Control, 1993, 57(1): 237-246
[22] H. Trinh and M. Aldeen, On the stability of linear systems with delayed perturbations[J]. IEEE Trans. Automat. Contr., 1994, AC-39(9): 1948-1951
[23] H. Trinh and M. Aldeen, Stability robustness bounds for linear systems with delayed perturbations[J]. IEEE Proc. Pt. D., 1995, 142(4): 345-350
[24] H.G. Chen, K.W. Han, Improved quantitative measures of robustness for multivariable systems[J]. IEEE Trans. Automat. Contr., 1994, AC-39(4): 807-810
[25]俞立,陈国定,杨马英,具有滞后摄动的线性系统鲁棒稳定性分析[J].控制理论与应用,1999, 16(4): 577-579
[26] L.H. Xie, Output feedback H∞control of systems with parameter uncertainty[J]. Int. J. Control, 1996, 63(4): 741-750
[27] F.H. Hsiao, Stabilization of uncertain time-delay systems with seres nonlinearities[J]. Int. J. Systems Sci., 1993, 24: 2175-2186
[28] T.J. Su, P.L. Liu, Robust stability of delay dependence for linear uncertain systems[J]. IEEE.Trans. Auto. Contr., 1992, 37: 1656-1659
[29] T.J. Su, P.L. Liu, Robust stability for linear uncertain time-delay systems with delay- dependence[J]. Int. J. Systems Sci., 1993, 24: 1067-1080
[30] B.G. Xu, Delay-dependent stability for linear uncertain time-delay systems[J]. Control Theory and Applications, 1996,13(4):426-430
[31] Y.G. Gu, S.C.Wang etc., On delay-dependent stability and decay estimate for uncertain systems with time- varying delay[J]. Technical Communique, 1998, 34(8): 1035-1039
[32] K. G u, Discretized LMI set in the stability problem for linear uncertain time-delay systems[J].Int. J. Control, 1997, 68(4): 923-934
[33] K. G u , A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems[J]. In t. J. Robust & Nonlinear Control, 1999, 9(1):1-4
[34] K. Gu, A further refinement of discretized Lyapunov functional method for the stability of time- delay systems[J]. Int. J. Control, 2001,74 (10): 967-976
[35] Q.L. Han, K. Gu, On robust stability of time-delay systems with norm-bounded uncertainty[J]. IEEE Trans. Automat. Contr., 2001,46(9):1426-1431
[36] E. Fridman, U. Shaked. Delay-dependent stability and H∞control: constant and time-varying delays[J]. In t. J. Control, 2003, 76(1): 4 8-60
[37] P. Park, A delay-dependent stability criterion for systems with uncertain time-invariant delays[J]. IEEE Trans. Automat. Contr., 1999, 44 (4): 876-877
[38] Y.S. Moon, P.Park, W.H. Kwon, et al. Delay-dependent robust stabilization of uncertain state- delayed systems[J]. Int. J. Control. 2001, 74 (14): 1 447-1455
[39] T.J.Su, C.G.Huang, Robust stability of delay dependence for linear uncertain systems[J]. IEEE Trans. Automa. Contr.,1992,37(10):1656-1659
[40] X. Li, C.E. de Souza, Delay-dependent robust stability and stabilization of uncertain linear delay systems: A Linear Matrix Inequality approach[J]. IEEE Trans. Automat. Contr., 1997, 42(8): 1144-1148
[41] Y.Y. Cao, Y.X. Sun, C .W. Cheng, Delay-dependent robust stabilization of uncertain systems with multiple state delays[J]. IEEE Trans. Automat. Contr., 1998, 43(11): 1608-1612
[42] P.L. Liu, T.J. Su, Robust stability of interval time-delay systems with delay dependence. Systems & Control Letters[J], 1998,33(4): 231-239
[43] Y.Y. Cao, J. Lam Computation of robust stability bounds for time-delay systems with nonlinear time-varying perturbations[J]. Int. J. Sys. Sci., 2000,31(3): 359-365
[44] J.H. Kim, Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty. IEEE Trans. Automat. Contr., 2001, 46(5): 789-792
[45] D.Yue, S. Won, An improvement on’Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty’[J]. IEEE Trans. Automat. Contr., 2002, 47(2): 407-408
[46] Y. Xia, Y. Jia, Robust stability functionals of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functions[J]. Int. J. Control, 2002, 75(16):1427-1434
[47] Y. Xia, Y. Jia, Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals[J]. Systems & Control Letters, 2003, 50(3): 183 -193
[48] D.Yue, Robust stabilization of uncertain systems with unknown input delay[J]. Automatica, 2004, 40(2): 331- 336
[49] L.L. Xiong, S.M. Zhong, J.K. Tian, Novel robust stability Criteria of uncertain neutral systems with discrete and distributed delays[J]. Chaos Solitons & Fractals, 2007, Available online at www.sciencedirect.com
[50] K. Gu, S.I. Niculescu, Additional dynamics in transformed time delay systems[J]. IEEE Trans. Automat. Contr., 2000, 45(3): 572-575
[51] K. Gu, S.I. Niculescu, Further remarks on additional dynamics in various model transformations of linear delay systems[J]. IEEE Trans. Automat. Contr., 2001, 46(3): 497-500
[52] E. Fridman, New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems[J]. Systems & Control Letters, 2001, 43(4): 309-319
[53] E. Fridman, U. Shaked, New bounded real lemma representations for time-delay systems and their applications [J]. IEEE Trans. Automat. Contr., 2001, 46 (12): 1973-1979
[54] E. Fridman, U. Shaked, An improved stabilization method for linear time-delay systems[J]. IEEE Trans. Automat. Contr., 2002, 47(11): 1931-1937
[55] E. Fridman, Stability of linear descriptor systems with delay: a Lyapunov-based approach[J]. J. Math. Anal. Appl., 2002, 273(1): 24-44
[56] E. Fridman, U. Shaked, On delay-dependent passivity[J]. IEEE Trans. Automat. Contr., 2002, 47(4): 664-669
[57] E. Fridman, U. Shaked, Parameter dependent stability and stabilization of uncertain time-delay systems[J]. IEEE Trans. Automat. Contr.l, 2003, 48(5): 861-866
[58] Y.S. Lee, Y.S. Moon, W.H. Kwon, et al., Delay-dependent robust H∞control for uncertain systems with a state-delay[J]. Automatica, 2004, 40(1): 65-72
[59] Q.L. Han A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays[J]. Automatica, 2004, 40(10): 1791-1796
[60] Q.L. Han, Stability criteria for a class of linear neutral systems with time-varying discrete and distributed delays[J]. IMA Journal of Math. Contr. and Info., 2003, 20(4): 371- 386
[61] Q.L. Han, Robust stability of uncertain delay-differential systems of neutral type[J]. Automatica,2002, 38(4): 718-723
[62] S.I. Niculescu, On delay-dependent stability under model transformations of some neutral linear systems[J]. Int. J. Control, 2001, 74(6): 608-617
[63] S.I. Niculescu, Optimizing model transformations in delay-dependent analysis of neutral systems: A control-based approach[J]. Nonlinear Analysis, 2001, 47(8): 5378-5390
[64] C.H.Lien, Stability and stabilization criteria for a class of uncertain neutral systems with time- varying delays [J]. Journal of Optimization Theory and Applications, 2005, 124: 637- 657
[65] Q.L. Han On robust stability of neutral systems with time-varying discrete delay and norm- bounded uncertainty[J]. Automatics, 2004, 40(6): 1087-1092
[66] P.L. Liu, On the stability of neutral-type uncertain systems with multiple time delays[J]. Int. J. Appl. Math. Comput. Sci., 2005, 15(2): 221-229
[67] B. Wang, S.M. Zhang, On novel stability criterion of neutral systems with time-varying delay[J]. Appl. Math. Compt., 2007, Available online at www.sciencedirect.com
[68] W.H. Chen, W.X. Zheng, Delay-dependent robust stabilization for uncertain neutral systems with distributed delays[J]. Automatic, 2007, 43: 95-104
[69] K.W. Yu, C.H. Lie, Stability critera for uncertain neutral systems with interval time-varying delays[J]. Chaos Soltion & Fractals, 2007, Available online at www.sciencedirect.com
[70] Y. Chen, A.K. Xue, et al., On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations[J]. Nonlinear Analysis, 2007, doi:10.1016/j.na. 2007.01.070
[71] L.G. Xiong, S.M. Zhong, J.K. Tian, Novel robust stability criteria of uncertain neutral systems with discrete and distributed delays[J]. Chaos Soltion & Fractals, 2007, Available online at www.sciencedirect.com
[72]何勇,自由权矩阵的时滞相关鲁棒稳定与镇定[D].中南大学,2004
[73] Y. He, M. Wu, et al., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays[J]. Systems & Control Letters, 2004, 51: 57-65
[74] M. Wu, Y. He, J.H. She, New delay-dependent stability criteria and stabilizing method for neutral systems[J]. IEEE Trans. Automat. Contr. 2004, 49: 2266-2271
[75] BerntΦksendal, Stochastic Differential Equations, An Introduction with Applications[M]. Fourth Edition, Springer-Verlag,北京:世界图书出版公司,1998
[76] R.Z. Hasminskii, Stochastic Stability of Differential Equations[M]. Netherlands: Sijthoff andNoordhoff, 1980
[77] V.B. Kolmanovskii, V.R. Nosov, Stability of Functional Differential Equations[M]. London: Acadenic Press, 1986
[78] S.-E.A Mhammed, Stochastic Functional Differential Equations[M]. New York: Longman, 1986
[79]胡宣达,随机微分方程稳定性理论[M].南京大学出版社,1986
[80]冯昭枢,随机系统的稳定性与镇定[D].华南理工大学,1990
[81]刘永清,冯昭枢,大型动力系统的理论与应用,卷4:随机·稳定与控制[M].华南理工大学出版社,1992
[82]刘永清,邓飞其,大型动力系统的理论与应用,卷10:随机系统的变结构控制[M].华南理工大学出版社,1992
[83] V.B. Kolmanoviskii, A. Myshkis, Applied Theory of Functional Differential Equations[M]. Dordrecht: Kluwer Academic Publishers, 1992
[84] X. Mao, Exponential Stability of Stochastic Differential Equations[M], New York: Marcel Dekker, 1994
[85] E.I. Verriest, Stabilization of deterministic and stochastic systems with uncertain time delays[J]. Proceedings of the 33th IEEE Conference on Decision and control, Lake Buene Vista (FL), 1994: 3829-3833
[86] E.I. Verriest, P. Florchinger, Stability of stochastic systems with uncertain time delays[J]. Systems & Control Letters, 1995, 24:41-47
[87] E.I. Verriest, Stability and stabilization of stochastic systems with distributed delays[J]. Proceedings of the 34th IEEE Conference on Decision and control, New Orleans(LA), 1995: 2205-2209
[88]邓飞其,冯昭枢,刘永清,时不变线性Ito ?随机系统均方稳定性的充分条件[J].自动化学报,1996, 22(4): 510-512
[89] T. Sasagawa, J.L. Willems, Parametrization method for calculating exact stability bounds of stochastic linear systems with multiplicative noise[J]. Automatica, 1996, 32(12): 1741-1747
[90] X. Mao, Exponential stability in mean square of neutral stochastic functional differential equations[J]. Syst. Contr. Letters, 1995, 26: 245-251
[91] X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations[J]. SIAM Journal on Mathematical Analysis, 1997, 28(2): 389-401
[92]廖晓昕,毛学荣,随机中立型微分方程稳定性[J].科学通报,1997, 42(10): 1117-1118
[93] X. Mao, Stochastic Differential Equations and Their Applications[M], Horwood Publlshing Limited, 1997
[94] X.X. Liao, X. Mao, Almost sure exponential stability of neutral stochastic differential equat- ions[J]. J. Math. Anal. & Appal. 1997, 212: 554-570
[95]沈轶,廖晓昕,随机中立型泛函微分方程指数稳定的Razumikhin型定理[J].科学通报,1998, 43(21): 2272-2275
[96] X. Mao, LaSalle-type theorems for stochastic differential delay equations[J]. J. Math. Anal. Appl., 1999, 236: 350-369
[97] K.Liu, X. Xia, On the exponential stability in mean square of neutral stochastic functional differential equations[J]. Systems & Control Letters, 1999, 37(4):207-215.
[98] P. Florchinger, Stability of some linear stochastic systems with distributed delays[J]. Proceedings of the 40th IEEE Conference on Decision and control, Orlando, Florida USA, 2001: 4744-4745
[99] X. Mao, A note on the LaSalle-type theorems for stochastic differential delay equations[J]. J. Math. Anal. Appl., 2002, 268: 125-142
[100] A.F. Ivanov, Y.I. Kazmerchuk, A.V. Swishchuk, Theory, stochastic stability and applications of stochastic delay differential equations: a survey of recent results[J]. Differential Equation and Dynamical Systems, 2003, 11:55-116
[101] E.K. Boukas, Control of stochastic systems with time-varying multiple time delays: LMI approach. Journal of Optimization Theory and Applications, 2003, 119(1): 19-36
[102]江明辉,沈轶,廖晓昕,中立型随机时滞系统的渐近稳定性[J].华中科技大学学报(自然科学版), 2005, 33(11): 71-73
[103] E.I. Verriest, Stochastic stability of a class of distributed delay systems[J], Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, 2005IEEE: 5048-5053
[104]张俊,沈轶等,中立型非线性随机时滞系统的渐近稳定性[J].华中科技大学学报(自然科学版), 2006, 34(10): 61-63
[105] W.H. Zhang, X.Z. Liu, et al., On stabilization for a class of nonlinear stochastic time-delay systems: a matrix inequality apporach[J]. Journal of Control Theory and Applications, 2006, 3:229-234
[106] Y. Shen, Q. Luo, X. Mao, The improved LaSalle-type theorems for stochastic functionaldifferential equations[J]. J. Math. Anal. Appl., 2006, 318: 134-154
[107] B. Ficak, Point delay methods applied to the investigation of stability for a class of distributed delay systems[J]. Systems & Control Letters, 2007, 56(3): 223-229
[108] J. Randjelovic, S.Jankovic,On the pth moment exponential stability criteria of neutral stochastic functional differential equations[J]. Journal of Mathematical Analysis and Applications, 2007, 326(1):266-280
[109] E.K. Boukas, H. Yang, Exponential stabilizability of stochastic systems with Markovian jumping parameters [J]. Automatica, 1999, 35: 1437-1441
[110] X. Mao, L. Shaikhet, Delay-dependent criteria for stochastic differential delay equations with Markovian switching[J]. Stochastic processes and Their Applications, 2000, 3(2): 87-101
[111] Y.Y. Cao, J. Lam, L.S. Hu, Delay-dependent stochastic stability and H∞analysis for time- delay systems with Markovian jumping parameters[J]. J. Franklin Institute, 2003, 340:423-434
[112] J.B.R. do Val, C. Nespoli, Stochastic stability for Markovian jump linear systems subject to a crucial failure event[J]. Proceeding of the American Control Conference, Denver, Colorado, 2003:4249-4254
[113] P. Bolzern, P. Colaneri, G. De Nicolao, On almost sure stability of continuous-time Markov jump linear systems[J]. Automatica, 2006, 42: 983-988
[114] X. Mao, Robustness of exponential stability of stochastic differential delay equations[J]. IEEE Trans. Auto mat. Contr., 1996, Ac-41: 442-447
[115] X. Mao, N. Koroleva, A. Rodkina, Robust stability of uncertain stochastic differential delay equations[J]. Syst. Contr. Lett., 1998, 35(5): 325-336
[116] X.X. Liao, X. Mao, Exponential stability of stochastic delay interval systems[J]. Syst. Contr. Lett., 2000, 7(2):307-328.
[117] S.L.Xie, L.H. Xie, Stabilization of a class of uncertain large-scale stochastic systems with time delay[J]. Automatica, 2000, 36: 161-167.
[118] D. Yue, S. Won, Delay dependent robust stability of stochastic systems with time delay and nonlinear uncertainies[J]. Electronics Letters, 2001, 37(15): 992-993
[119] C.Y. Lu, J.S.H. Tsai, T.J. Su, An LMI-based approach for robust stabilization of uncertain stochastic systems with times-varying delays[J]. IEEE Trans, Automat. Contr., 2003, 48(2): 286-289
[120]包俊东,时滞随机系统的鲁棒稳定性、镇定与控制[D].华南理工大学学报, 2004
[121] C.Y. Lu, T.J. Su, J.S.H. Tsai, On robust stabilization of uncertain stochastic time-delay systems—an LMI- based approach[J]. Journal of the Franklin Institute, 2005, 342: 473-487
[122] W.H. Chen, Z.H. Guan, X.M.Lu, Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach[J]. Syst.Contr.Lett., 2005, 54(6): 547-555
[123] G.L. Wei, Z.D. Wang, et al. Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances[J]. Systems & Control Letters, 2007, 56: 623-633
[124] Z.D. Wang, Y.R. Liu, et al., Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays[J], Physics Letters A, 2006, 354(4): 288-297
[125] Z.D. Wang, J.A. Fang, X.H. Liu, Global stability of stochastic high-order neural networks with discrete and distributed delays[J]. Chaos Solitons & Fractals, 2006,
[126] W.W. Su, Y.M. Chen, Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays[J]. Communications in Nonlinear Science and Numerical Simulation, 2007,
[127] S.Y. Xu, P. Shi, Y.M. Chu, et al., Robust stochastic stabilization and H∞control of uncertain neutral stochastic time-delay systems[J]. Journal of Mathematical Analysis and Applications, 2006, 314(1): 1-16
[128]江明辉,沈轶,廖晓昕,不确定中立线性随机时滞系统的鲁棒稳定性[J].应用数学和力学, 2007, 28(6):741-748
[129] E.K. Boukas, P. Shi, stochastic stability and guaranteed cost control of discrete time uncertain systems with Markovian jumping parameters[J]. Int. J. Control, 1998, 8: 1155-1156
[130] X. Mao, Robustness of stability of stochastic differential equations with Marlovian switching[J]. Stability and Control: Theory and Applications, 2000, 3(1): 48-61
[131] Z.D. Wang, H.Qiao, K.J. Burnham, On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters[J]. IEEE Trans. Automat. Contr., 2002, 47(4): 640-646
[132] J. D. Bao, F.Q. Deng, Q. Luo, Robust Stochastic, Stabilization of uncertain Markovian jumping systems with distributed time-delay based on LMI’s approach[J]. Proceedings of The International Symposium on Intelligent Control, Houston USA, 2003: 484-489
[133] Z.H. Guan, W.H. Chen, J.X. Xu, Delay-dependent stability and stabilizability of uncertain jump bilinear staochastic systems with mode-depentent time-delays[J]. Int. J. Syst. Contr. Sci., 2005, 36(5): 275-285
[134] J.L.Deng, Control Problems of Grey Systems[J]. Syst. Contr. Lett., 1982, 1(5): 288-294
[135]邓聚龙,灰色控制系统[J].华中工学院学报,1982, 10(3): 9-18
[136]刘凯,灰色集合于灰色系统的稳定性.华中工学院学报,1982, 10(3): 23-25
[137]陈绵云,灰色系统的稳定性与镇定问题[J].模糊数学,1985, 2: 101-106
[138]邓聚龙,周朝顺,灰色线性定常系统的反馈镇定及其稳定性充分判据[J].模糊数学,1985, 2: 107-110
[139] C.S.Zhou, J.L.Deng, The stability of the grey linear System[J]. Int. J. Control, 1986, 43(1): 313-320
[140]周朝顺,灰色系统稳定性判据[J].华中工学院学报,1986, 14(1): 23-26
[141]邓聚龙,周朝顺,灰色系统稳定性充分条件及其在学习时变系统稳定性分析中的应用[J].信息与控制,1987, 4: 24-27
[142]周朝顺,阙泰林,互联灰色动态系统稳定性的充分条件[J].华中理工大学学报,1989, 17(2): 83-87
[143]何灿芝,陈强,关于灰色线性时滞系统的稳定性[J].湖南大学学报,2001, 28(1): 5-7
[144]万上海,周宗福,灰色线性时滞系统的稳定性[J].安徽工程科技学院学报,2005, 20(2): 63-65
[145]周朝顺,邓聚龙,阙泰林,灰色离散系统的稳定性充分条件[J].华中理工大学学报, 1988, 16(4): 141-145
[146] C.S.Zhou, J.L.Deng, Stability analysis of grey discrete-time systems[J]. IEEE Trans. Auto. Contr., 1989, 34(2): 173-175
[147]彭晓林,罗晓,灰色离散系统稳定与不稳定的代数判据[J].应用数学,1991, 4(2): 76-81
[148]陈菊芳,非线性灰色离散系统零解的稳定性[J].应用数学学报,1995, 18(1): 123-128
[149]李建平,灰色时变离散系统的稳定性分析[J].经济数学,1996, 13(2): 92-95
[150]刘碧玉,灰色时滞离散大系统的稳定性[J].系统工程,1996, 14(3): 15-17
[151]周宗福,郑祖庥,非线性灰色时滞离散系统的稳定性[J].应用数学学报,2004, 27(2): 371-374
[152] Q.X. Li, S.F. Liu, The foundation of the grey matrix and the grey input-output analysis[J], Appl. Math. Modell., 2008, 32(3): 267-291
[153]苏春华,刘思峰,灰色随机线性时滞系统的渐近稳定性[J].控制与决策, 2008, 23(5): 571-574
[154]邓聚龙,灰理论基础[M].武汉:华中科技大学出版社,2002
[155]刘思峰,党耀国,方志耕,灰色系统理论及其应用[M].北京:科学出版社,2004
[156] V. D. Mil man, A. D. M yshkis, On the stability of motion in presence of impulses[J]. Siberian Math J., 1960: 233- 237.
[157] D.D. Bainov, P.S. Simeonov, System with impulse effect, Stability, Theory and Applications[M], New York: Wiley, 1989
[158] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations [M] . Singapore: World Scientific, 1989
[159] A.M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, Singapore: World Scientific, 1995
[160] A. V. Anokhin, On linear impulsive systems for functional differential equations[J]. Soviet Math Dokl, 1986, 33: 220-223
[161] S. I. Gurgula, Investigation of the stability of solutions of impulsive systems by Lyapunov’s second method[J]. Ukrainian Math. J. 1982, 1: 100-103
[162] Angelova J ,Dishliev A. Continuous dependence and uniform stability of solution of impulsive differential equation on impulsive moment s[J] . Nonlinear Analysis ,1997 ,28: 825-835
[163] M. U. Akhmetov, A. Zafer, Stability of the zero solution of impulsive differential equations by the Lyapunov second method[J]. Journal of Mathematical Analysis and Applications, 2000, 248: 69-82
[164] A A. Soliman, On stability of perturbed impulsive differential systems[J]. Applied Mathematics and Computation, 2002 ,133 :105～117
[165] A A. Soliman, Stability criteria of impulsive differential systems[J] . Applied Mathematics and Computation, 2003, 134: 445～457
[166] J.R. Yan, J.H. Shen, Impulsive stabilization of functional differential equations by Lyapunov–Razumikhin functions[J]. Nonlinear Analysis, 1999, 37: 245–255
[167] L.M.Stamova, G.T. Stamov, Lyapunov-Razumikhin method for impulsive differential equations and applications to the population dynamics[J]. J. Comput. Appl. Math. , 2001, 130: 163～171.
[168] X. Liu, G. Ballinger, Uniform asymptotic stability of impulsive delay differential equations[J]. Computers and Mathematics with Applications ,2001 ,41 :903～915
[169] Y.P. Xing, M.A. Han, A new approach to stability of impulsive functional differential equations[J]. Appl. Math. Comput., 2004, 151: 835–847
[170] K. Liu, X.L. Fu, Stability of functional differential equations with impulses[J]. J. Math. Anal. Appl. 2007, 328: 830–841
[171] Z. Kamont, J. Turo, B. Zubik-Kowal, Differential and difference inequalities generated by mixed problems for hyperbolic functional differential equations with impulses[J]. Appl. Math. Comput., 1996, 80: 127–154
[172] Z. Guan, Impulsive inequalities and stability of large scale singular measure differential systems with unbounded delays[J]. Dyn. Contin. Discrete Impuls. Syst. 1997, 3: 113–130
[173] X. Liu, X. Shen, Y. Zhang, A comparison principle and stability for large-scale impulsive delay differential systems[J]. Anziam J., 2005, 47: 203–235
[174] D. Xu, Z. Yang, Impulsive delay differential inequality and stability of neural networks[J]. J. Math. Anal. Appl. 2005, 305: 107–120
[175]D.Y. Xu, Z.G. Yang, Z.C. Yang, Exponential stability of nonlinear impulsive neutral differential equatons with delays [J]. Nonlinear Analysis, 2007, 67: 1426-1439
[176]侯振挺,李俊平等,随机脉冲泛函微分方程理论[J].长沙铁道学院学报,2001, 19(3): 1-5
[177] H.J. Wu, J.T. Sun, p-Moment stability of stochastic differential equations with impulsive jump and Markovian switching[J]. Autonatica, 2006, 42: 1753-1759
[178] Z.G. Yang, D.Y. Xu, L. Xiang, Exponential p-stability of impulsive stochastic differential equations with delays [J]. Physics Letters A, 2006, 359: 129-137
[179] Z.G. Yang, D.Y. Xu, Mean square exponential stability of impulsive stochastic differential equations[J]. Applied Mathematics Letters, 2007, 20: 938-945