Stabilization for Markovian Jump Systems with Additive Time-varying Delays

Abstract

Abstract-In this paper, the problem of stabilization for Markovian jump systems with additive time-varying delays is considered. First of all, by constructing a new Lyapunov functional with triple integral terms, using new inequalities, convex combination technique and combining with other analytical techniques, the stochastically stability and stabilization conditions of the Markovian jump systems in terms of linear matrix inequalities with lower conservatism are obtained. Then, the controller of the closed-loop system is designed by the transformation technique of inequalities. Finally, a numerical example is given to verify the effectiveness of the provided method and the superiority of the results.