Delay-Dependent Stability of Impulsive Stochastic Systems with Multiple Delays

This paper associates with stability analysis of linear impulsive stochastic delay systems (ISDSs). Although many conclusions about the stability of ISDSs have been obtained based on Lyapunov's method, relatively few research theories about delay-dependent stability with less conservativeness have been established. Therefore, we introduce an appropriate Lyapunov-Krasovskii functional (LKF) to work out this problem, and a novel delay-dependent exponential stability theorem is first deduced. On the other hand, when mean-square stability is considered, we present delay-dependent stability conditions, it is of interest to note that the proposed conditions do not depend on the size of delays in the diffusion term, which solves the problems of determining the mean-square stability of ISDSs for which the diffusion term delays are not available. In the end, two numerical examples are carried out to verify the feasibility of our conclusions.