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Delay-interval-dependent robust stability results for uncertain stochastic systems with Markovian jumping parameters. (English) Zbl 1227.93124
Summary: This paper is concerned with the robust stability analysis of Markovian jumping uncertain stochastic systems with interval time-varying delays. The parametric uncertainties which appear in all system matrices are assumed to be norm bounded. A new Markovian jumping matrix P i is introduced for deriving the stability results. Based on the Lyapunov stability theory and stochastic analysis technique, new improved delay-dependent robust stability criteria are derived by considering the relationship among the time-varying delay, its upper bound and their difference without ignoring any terms. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.
MSC:
93E15Stochastic stability
93D09Robust stability of control systems
93E03General theory of stochastic systems
60J75Jump processes
References:
[1]Gu, K.; Kharitonov, L.; Chen, J.: Stability of time delay systems, (2003)
[2]Peng, C.; Tian, Y. C.: Delay range-dependent robust stability criteria for uncertain systems with interval time-varying delay, Journal of computational and applied mathematics 214, 480-494 (2008) · Zbl 1136.93437 · doi:10.1016/j.cam.2007.03.009
[3]Li, T.; Gua, L.; Zhang, Y.: Delay range-dependent robust stability and stabilization for uncertain systems with time-delay, International journal of robust and nonlinear control 18, 1372-1387 (2008)
[4]Jiang, X.; Han, Q. L.: Delay-dependent robust stability for uncertain linear systems with interval time-varying delay, Automatica 42, 1059-1065 (2006) · Zbl 1135.93024 · doi:10.1016/j.automatica.2006.02.019
[5]He, Y.; Wang, Q. G.; Lin, C.; Wu, M.: Delay range-dependent stability for systems with time-varying delay, Automatica 43, 371-376 (2007) · Zbl 1111.93073 · doi:10.1016/j.automatica.2006.08.015
[6]Mao, X. R.; Shaikhet, L.: Delay-dependent stability criteria for stochastic differential delay equations with Markovian switching, Stability and control: theory and applications 3, 87-101 (2000)
[7]Wei, G. L.; Wang, Z. D.; Shu, H. S.; Fang, J. A.: Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances, Systems and control letters 56, 623-633 (2007) · Zbl 1156.60318 · doi:10.1016/j.sysconle.2007.03.009
[8]Xu, S. Y.; Chen, T. W.: Robust H control for uncertain stochastic systems with state delay, IEEE transactions on automatic control 47, 2089-2094 (2002)
[9]Lu, C. Y.; Tsai, J. S. H.; Jong, G. J.; Su, T. J.: An LMI-based approach for robust stabilization for uncertain stochastic systems with time-varying delays, IEEE transactions on automatic control 48, 286-289 (2003)
[10]Xu, S. Y.; Lam, J.; Chen, T. W.: Robust H control for uncertain discrete stochastic time-delay systems, Systems and control letters 51, 203-215 (2004) · Zbl 1157.93372 · doi:10.1016/j.sysconle.2003.08.004
[11]Chen, W. H.; Guan, Z. H.; Lu, X. M.: Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach, Systems and control letters 54, 547-555 (2005) · Zbl 1129.93547 · doi:10.1016/j.sysconle.2004.10.005
[12]Yan, H. C.; Huang, X. H.; Zhang, H.; Wang, M.: Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay, Chaos solitons and fractals 40, 1668-1679 (2009) · Zbl 1198.93171 · doi:10.1016/j.chaos.2007.09.049
[13]Chen, Y.; Xue, A.; Zhou, S.; Lu, R.: Delay-dependent robust control for uncertain stochastic time-delay systems, Circuits systems and signal processing 27, 447-460 (2008) · Zbl 1179.93169 · doi:10.1007/s00034-008-9037-8
[14]Yue, D.; Fang, J.; Won, S.: Delay-dependent robust stability of stochastic uncertain systems with time delay and Markovian jump parameters, Circuits systems and signal processing 22, 351-365 (2003) · Zbl 1048.93095 · doi:10.1007/s00034-004-7036-y
[15]Yue, D.; Han, Q. L.: Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity and Markovian switching, IEEE transactions on automatic control 50, 217-222 (2005)
[16]Y. Zhang, Y. He, M. Wu, Improved delay-dependent robust stability for uncertain stochastic systems with time-varying delays, in: Proceedings of 27th Chinese Control Conference, China, 2008.
[17]Zhang, Y.; He, Y.; Wu, M.: Delay-dependent robust stability for uncertain stochastic systems with interval time-varying delay, Auto automatica sinica 35, 577-582 (2009) · Zbl 1212.93322 · doi:10.3724/SP.J.1004.2009.00577
[18]He, Y.; Zhang, Y.; Wu, M.; She, J. H.: Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay, International journal of robust and nonlinear control 20, 16-26 (2010) · Zbl 1192.93125 · doi:10.1002/rnc.1412
[19]Rakkiyappan, R.; Balasubramaniam, P.: Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays, Nonlinear analysis: hybrid systems 3, 408-417 (2009) · Zbl 1194.93191 · doi:10.1016/j.nahs.2009.02.008
[20]Wang, Z.; Liu, Y.; Liu, X.: State estimation for jumping recurrent neural networks with discrete and distributed delays, Neural networks 22, 41-48 (2009)
[21]Tang, Y.; Fang, J. A.; Miao, Q. Y.: Synchronization of stochastic delayed neural networks with Markovian switching and its application, International journal of neural systems 19, 43-56 (2009)