Delay‐dependent stability criterion and H∞ analysis for Markovian jump systems with time‐varying delays

This paper deals with the problems of stochastic stability and H∞ analysis for Markovian jump linear systems with time-varying delays. In terms of linear matrix inequalities, a less conservative delay-dependent stability criterion for Markovian jump systems is proposed by constructing a different Lyapunov-Krasovskii functional and introducing improved integral-equalities approach, and a sufficient condition is derived from the H∞ performance. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

[1]  Jing Wu,et al.  Delay-dependent robust stability and H∞ control for jump linear systems with delays , 2006, Syst. Control. Lett..

[2]  Z. Liu,et al.  Delay-dependent robust stability and H8 control of jump linear systems , 2001 .

[3]  Shengyuan Xu,et al.  H∞H∞ output feedback control for uncertain stochastic systems with time-varying delays☆ , 2004 .

[4]  Z. Guan,et al.  Delay-dependent output feedback stabilisation of Markovian jump system with time-delay , 2004 .

[5]  Shengyuan Xu,et al.  Hinfinity output feedback control for uncertain stochastic systems with time-varying delays , 2004, Autom..

[6]  C. Pinello,et al.  Automotive engine control and hybrid systems: challenges and opportunities , 2000, Proceedings of the IEEE.

[7]  Zhi-Hong Guan,et al.  PASSIVE CONTROL SYNTHESIS FOR UNCERTAIN MARKOVIAN JUMP SYSTEMS WITH MULTIPLE MODE-DEPENDENT TIME-DELAYS , 2008 .

[8]  E. Boukas,et al.  Mean square stochastic stability of linear time-delay system with Markovian jumping parameters , 1998, IEEE Trans. Autom. Control..

[9]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[10]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[11]  E. Sánchez,et al.  OPTIMAL LINEAR FILTERING FOR SYSTEMS WITH MULTIPLE STATE AND OBSERVATION DELAYS , 2007 .

[12]  Yong-Yan Cao,et al.  Delay-dependent stochastic stability and H∞ analysis for time-delay systems with Markovian jumping parameters , 2003, J. Frankl. Inst..

[13]  Hiroshi Fujisaki,et al.  On Correlation Values of M-Phase Spreading Sequences of Markov Chains , 2001 .

[14]  Jun Zhao,et al.  Output feedback variable structure control for a class of uncertain switched systems , 2009 .

[15]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  El-Kébir Boukas,et al.  Delay-dependent robust stability and H/sub /spl infin// control of jump linear systems with time-delay , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).