Exponential l 2 - l ∞ stochastic stability analysis for discrete-time switching Markov jump linear systems

The problem of exponential l 2 - l ∞ stochastic stability is considered in this paper for a class of discrete-time switching Markov jump linear systems(S-MJLS). Firstly, the definition of exponential l 2 - l ∞ stochastic stability is introduced. Then, by virtue of the average dwell time approach, the stochastic stability criteria are presented with an exponential l 2 - l ∞ performance index and a decay rate. A numerical example is provided to demonstrate the effectiveness of the obtained results.

[1]  D. Wilson.  Convolution and Hankel operator norms for linear systems , 1989 .

[2]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[3]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[4]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[5]  Shengyuan Xu,et al.  Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching , 2005 .

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

[7]  E. Boukas,et al.  Exponential H∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach , 2008 .

[8]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[9]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[10]  Ligang Wu,et al.  Average dwell time approach to L 2 -L∞1 control of switched delay systems via dynamic output feedback , 2009 .

[11]  Patrizio Colaneri,et al.  Markov Jump Linear Systems with switching transition rates: Mean square stability with dwell-time , 2010, Autom..

[12]  Linlin Hou,et al.  Robust l2−l∞ state feedback control for uncertain discrete-time switched systems with mode-dependent time-varying delays† , 2010 .