Exponential Stabilization of Markov Jump Systems with Mode-Dependent Mixed Time-Varying Delays and Unknown Transition Rates

Abstract

This paper investigates the problem of exponential stability in mean square sense for stochastic Markov jump systems with mixed time-varying delays and partly unknown transition rates. By employing a class of appropriate stochastic Lyapunov functionals, the analysis process of stability for stochastic Markov jump systems can be effectively carried out. Based on the linear matrix inequalities technique, the mean square exponential stability criteria are presented for stochastic Markov jump systems with partly unknown transition rates. Furthermore, by expanding this case to uncertain Markov jump systems, we derive the sufficient conditions for guaranteeing the stability of uncertain Markov jump systems. A numerical example is presented to illustrate the effectiveness of the proposed results.