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.