Stochastic admissibility and stabilization of singular Markovian jump systems with multiple time-varying delays

Abstract

This paper is concerned with stochastic admissibility and state feedback stabilization for a class of singular Markovian jump systems with multiple time-varying delays. The singular matrix E with both modedependent and mode-independent is considered in the system. Firstly, based on Lyapunov functional method and free-weighting matrix method, sufficient condition is presented in the form of linear matrix inequalities (LMIs) to guarantee the considered system to be stochastically admissible. Secondly, by state feedback controller, sufficient condition is derived in terms of strict LMIs to ensure the closed-loop system to be stochastically stabilizable. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.