Delayed-state-feedback Exponential Stabilization of Stochastic Markovian Jump Systems with Mode-dependent Time-varying State Delays

In this paper, an improved mean-square exponential stability condition and delayed-state-feedback controller for stochastic Markovian jump systems with mode-dependent time-varying state delays are obtained. First, by constructing a modified Lyapunov-Krasovskii functional, a mean-square exponential stability condition for the above systems is presented in terms of linear matrix inequalities (LMIs). Here, the decay rate can be a finite positive constant in a range and the derivative of time-varying delays is only required to have an upper bound which is not required to be less than 1. Then, based on the proposed stability condition, a delayed-state-feedback controller is designed. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.