Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays

This paper studies the problem of the robustly exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays. The contribution of this paper is two-fold. Firstly, by constructing a modified Lyapunov functional and using free-weighting matrices technique, some delay-dependent robustly exponential stability criteria of such systems are obtained in terms of linear matrix inequalities (LMIs), which are less conservative than some existing ones. Secondly, a state feedback controller is designed, which can guarantee the robustly exponential stability of the uncertain closed-loop systems. Some illustrative numerical examples are given to demonstrate the reduced conservatism and applicability of the obtained results.

[1]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[2]  E. Feron,et al.  History of linear matrix inequalities in control theory , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[3]  James Lam,et al.  Robust H∞ control of uncertain Markovian jump systems with time-delay , 2000, IEEE Trans. Autom. Control..

[4]  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).

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

[6]  Wook Hyun Kwon,et al.  Robust stabilization of uncertain input-delayed systems using reduction method , 2001, Autom..

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

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

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

[10]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

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

[12]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

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

[14]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

[15]  James Lam,et al.  Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Dong Yue,et al.  Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching , 2005, IEEE Transactions on Automatic Control.

[17]  Shengyuan Xu,et al.  A new LMI condition for delay-dependent asymptotic stability of delayed Hopfield neural networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  James Lam,et al.  Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers , 2006, Autom..

[19]  Shengyuan Xu,et al.  Robust stabilization of Markovian delay systems with delay-dependent exponential estimates , 2006, Autom..

[20]  F. Gouaisbaut,et al.  DELAY-DEPENDENT STABILITY ANALYSIS OF LINEAR TIME DELAY SYSTEMS , 2006 .

[21]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

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

[23]  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.

[24]  Li Ma,et al.  Mean-square exponential stability of stochastic Markovian jump systems with mode-dependent time-varying delays , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[25]  Georgi M. Dimirovski,et al.  Stabilisation and L 2-gain analysis for a class of uncertain switched non-linear systems , 2009, Int. J. Syst. Sci..

[26]  Huijun Gao,et al.  New results on stabilization of Markovian jump systems with time delay , 2009, Autom..

[27]  Bing Chen,et al.  Delay-dependent stability analysis and controller synthesis for Markovian jump systems with state and input delays , 2009, Inf. Sci..

[29]  Georgi M. Dimirovski,et al.  Robust H ∞ sliding mode control for a class of uncertain switched delay systems , 2009, Int. J. Syst. Sci..

[30]  Jun Zhao,et al.  Adaptive Variable Structure Control for Uncertain Switched Delay Systems , 2010, Circuits Syst. Signal Process..

[31]  Li Ma,et al.  Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays: Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays , 2010 .

[32]  Meng Li,et al.  Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays , 2010 .

[33]  Shengyuan Xu,et al.  Delay-dependent H∞ filtering for stochastic systems with Markovian switching and mixed mode-dependent delays , 2010 .

[34]  Hongye Su,et al.  Delay-dependent H∞ filtering for singular Markovian jump time-delay systems , 2010, Signal Process..

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

[36]  Jie Zhang,et al.  Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices , 2011, Autom..

[37]  Hyo-Sung Ahn,et al.  Special issue on “iterative learning control” , 2011 .