一类广义混杂系统的随机稳定性及稳定化

doi:10.3969/j.issn.1001-2400.2010.05.016

Abstract

Abstract:

Based on the method combining the techniques of the multiple Lyapunov function and stochastic generalized Lyapunov function, a necessary and sufficient condition is derived for discrete-time singular hybrid systems with the time-homogenous finite state Markov chain without using the restricted equivalent property of singular systems. The condition is given in terms of coupled generalized Lyapunov equations (CGLEs) such that the solution of the systems is stochastically stable. The equations can be solved by changing them into strict linear matrix inequalities (SLMIs). The result is extended to solve the stabilization problem and the design of a state-feedback controller. A numerical example shows the effectiveness of the proposed approach.

Key words: discrete-time singular hybrid systems, coupled generalized Lyapunov equations, stochastic systems, stability, stabilization

YANG Ying;LI Jun-min;CHEN Guo-pei. Stochastic stability and stabilization for a class of singular hybrid systems[J].J4, 2010, 37(5): 866-871.

References

[1] Decarlo R A, Branicky M S, Pettersson S, et al. Perspective and Results on the Stability and Stabilizability of Hybrid Systems [J] . Proceedings of the IEEE, 2000, 88(7): 1069-1082.
[2] Liu B, Hill D J. Comparison Principle and Stability of Discrete-time Impulsive Hybrid Systems [J] . IEEE Trans on Circuits and Systems, 2009, 56(1): 233-245.
[3] Cai C, Teel A. Characterizations of Input-to-state Stability for Hybrid Systems [J] . Automatica, 2009, 58(1): 47-53.
[4] 陈国培, 李俊民, 杨莹. 一类不确定脉冲混合系统的非脆弱控制器设计[J] . 西安电子科技大学学报, 2008, 35(1): 65-70.
Chen Guopei, Li Junmin, Yang Ying. Design Methods for Non-fragile Controllers for a Class of Uncertain Impulsive Hybrid Syste-ms[J] . Journal of Xidian University, 2008, 35(1): 65-70.
[5] Ji Y, Chizeck H J. Controllability, Stability and Continuous-time Markovian Jump Linear Quadratic Control [J] . IEEE Trans on Automatic Control, 1990, 35(7): 777-788.
[6] Zhang L, Boukas E K. Stability and Stabilization of Markovian Jump Linear Systems with Partly Unknown Transition Probabilities [J] . Automatica, 2009, 45(2): 463-468.
[7] De Souza C E. Robust Stability and Stabilization of Uncertain Discrete-time Markovian Jump Linear Systems [J] . IEEE Trans on Automatic Control, 2006, 51(5): 836-841.
[8] Sathananthan S, Adetona O, Beane C, et al. Feedback Stabilization of Markov Jump Linear Systems with Time-Varying Delay [J] . Stochastic Analysis and Applications, 2008, 26(3): 577-594.
[9] Ishhara J Y, Terra M H. On the Lyapunov Theorem for Singular Systems [J] . IEEE Trans on Automatic Control, 2002, 47(11): 1926-1930.
[10] Masubuchi I, Kamitane Y, Ohara A, et al. H_∞ Control for Descriptor Systems: a Matrix Inequalities Approach [J] . Automatica, 1997, 33(4): 669-673.
[11] Xu S, Lam J. Robust Control and Filtering of Singular Systems [M] . Berlin: Springer, 2006.
[12] Boukas E K. On Robust Stability of Singular Systems with Random Abrupt Changes [J] . Nonlinear Analysis, 2005, 63(3), 301-310.
[13] Fu Yanming, Duan Guangren. Robust Guaranteed Cost Observer for Uncertain Descriptor time-delay Systems with Markovian Jumping Parameters [J] . Acta Automatica Sinica, 2005, 31(3): 149-153.
[14] Boyd S, Ghaoui E I, Feron E, et al. Linear Matrix Inequalities in System and Control Theory [M] . Philadelphia: SIAM, 1994.
[15] Xia Y Q, Zhang J H, Boukas E K. Control for Discrete Singular Hybrid Systems [J] . Automatica, 2008, 44(10): 2635-2641.
[16] Xu S Y, Lam J. Robust Stability and Stabilization of Discrete Singular Systems: an Equivalent Characterization [J] . IEEE Trans on Automatic Control, 2004, 49(4): 568-574.
[17] Xie L. Output Feedback H_∞ Control of Systems with Parameter Uncertainty [J] . Int J Control, 1996(63): 741-750.

Stochastic stability and stabilization for a class of singular hybrid systems

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