Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays

This paper deals with the problems of delay-dependent robust Hinfin 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 Hinfin control and Hinfin 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 Hinfin 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.