Further improvement of delay-dependent stability for Markov jump systems with time-varying delay

The problem of stochastic stability for a class of Markov jump systems with time-varying delay is considered in this paper. By some zero equations, without using model transformation or bounding for cross terms, delay-dependent stochastic stability conditions for Markov jump systems have already been obtained in the literature. But those conditions are rather conservative and do not guarantee stability for a system with a wide region. In order to get less conservative stability criteria, we choose a new type Lyapunov functional and some zero equations. Furthermore, those results are extended to the robustly stochastic stability for the system with two types of uncertainties. All the results are presented in the form of strict linear matrix inequalities (LMIs). Finally, several numerical examples are presented to illustrate the effectiveness and the benefit of the results obtained in this paper.