Delay-Dependent H Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays

• Published in: IEEE transactions on circuits and systems. 1, Fundamental theory and applications Fundamental theory and applications, 2007-09, Vol.54 (9), p.2070-2077
• Main Authors: Shengyuan Xu, Lam, J., Xuerong Mao
• Format: Article
• Language: English
• Subjects: Control systems; Delay; delay-dependent stability; Filtering; H_{\infty } control; H_{\infty } filtering; Linear matrix inequalities; Linear systems; Markovian jump systems; Nonlinear filters; output feedback; Robust control; Stochastic systems; Time varying systems; time-delay systems; Uncertain systems
• ISSN: 1549-8328; 1057-7122; 1558-0806
• DOI: 10.1109/TCSI.2007.904640

This paper deals with the problems of delay-dependent robust H infin control and filtering for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian delay systems are obtained by introducing some slack matrix variables. The conservatism caused by either model transformation or bounding techniques is reduced. Based on the proposed BRL, sufficient conditions for the solvability of the robust H infin control and H infin filtering problems are proposed, respectively. Dynamic output feedback controllers and full-order filters, which guarantee the resulting closed-loop system and the error system, respectively, to be stochastically stable and satisfy a prescribed H infin performance level for all delays no larger than a given upper bound, are constructed. Numerical examples are provided to demonstrate the reduced conservatism of the proposed results in this paper.