On almost sure stability and stabilization of stochastic delay systems with Markovian switching

This paper is concerned with the problems of almost sure (a.s.) stability and stabilization for stochastic systems with Markovian switching (SSMS) and time-varying delays. Some sufficient criteria on the stability for the underlying nonlinear stochastic systems is derived in terms of continuous semimartingale convergence theorem and Doob´s martingale inequality. The purpose of stabilization is to design linear state feedback control laws in the drift part so that the resulting closed-loop system is almost surely (a.s.) stable. Two numerical simulation examples are exploited to verify the effectiveness of the theoretical results.