New stochastic stability criteria for Markovian jump systems with mode-dependent time-varying-delays

Purpose – As a class of stochastic hybrid systems, Markovian jump systems have been extensively studied in the past decades. In light of some results obtained on this topic. The purpose of this paper is to investigate the stability problems for delayed Markovian jump systems.Design/methodology/approach – The time‐varying‐delays considered in this paper are switched synchronously with system mode. Based on stochastic Lyapunov theory, the delay‐dependent stability conditions are developed by using some linear matrix inequality techniques. To obtain better stability criteria, the different Lyapunov‐Krasovskii functional is chosen and an important inequality is introduced.Findings – Numerical examples show that the resulting criteria in this paper have advantages over some previous ones in that they involve fewer matrix variables, but have less conservatism. Furthermore, they only involve the matrix variables appeared in the Lyapunov functional. Therefore, there are no additional matrix variables coupled with...

[1]  E. Boukas,et al.  Robust Stability and Stabilizability of Markov Jump Linear Uncertain Systems with Mode-Dependent Time Delays , 2001, ACC.

[2]  Zhi-Hong Guan,et al.  Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays , 2003, IEEE Trans. Autom. Control..

[3]  Yong-Yan Cao,et al.  Delay‐dependent filtering design for time‐delay systems with Markovian jumping parameters , 2007 .

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

[5]  Xudong Zhao,et al.  Delay‐dependent stability criterion and H∞ analysis for Markovian jump systems with time‐varying delays , 2011 .

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

[7]  El-Kébir Boukas.  Singular linear systems with delay: ℋ︁∞ stabilization , 2007 .

[8]  K. Khorasani,et al.  A geometric approach to robust Fault Detection and Isolation of discrete-time Markovian jump systems , 2008, 2008 American Control Conference.

[9]  Shuzhi Sam Ge,et al.  Robust Output Feedback H∞ Control of Uncertain Markovian Jump Systems with Mode-Dependent Time-Delays , 2006, 2006 Chinese Control Conference.

[10]  El-Kébir Boukas,et al.  Control of Singular Systems with Random Abrupt Changes , 2008 .

[11]  Ning Chen,et al.  Robust decentralized H∞ control of multi-channel uncertain descriptor systems with time-delay , 2007, 2007 IEEE International Conference on Control Applications.

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

[13]  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.

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

[15]  Hanyong Shao.  Delay-range-dependent robust H∞ filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters , 2008 .

[16]  Yun Zou,et al.  Robust exponential stabilization for Markovian jump systems with mode-dependent input delay , 2007, Autom..

[17]  Yuesheng Luo,et al.  Further improvement of delay-dependent stability for Markov jump systems with time-varying delay , 2008, 2008 7th World Congress on Intelligent Control and Automation.

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

[19]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[20]  E. Boukas,et al.  Delay-dependent stability and output feedback stabilisation of Markov jump system with time-delay , 2002 .

[21]  Xudong Zhao,et al.  Delay-dependent robust control for uncertain stochastic systems with Markovian switching and multiple delays , 2010 .

[22]  H. Kushner.  Stochastic Stability and Control , 2012 .