Robust Stability of Stochastic Markovian Switching Delay Systems

This paper investigates robust asymptotic mean-square stability for uncertain stochastic delay systems with Markovian switching. Two types of parametric uncertainties are considered, i.e. Lipschitz nonlinear uncertainties and norm-bounded uncertainties. Based on introducing an auxiliary vector, an integral inequality in stochastic context is obtained. By this stochastic integral inequality, delay-dependent stochastic stability conditions for uncertain stochastic Markovian delay systems are developed. The results are derived by employing Lyapunov-Krasovskii method and presented in terms of linear matrix inequalities (LMIs). A numerical example and computational complexity analysis are provided to show the advantage of the method.