Exponential Stability of Impulsive Stochastic Functional Differential Systems with Delayed Impulses

Abstract

A class of generalized impulsive stochastic functional differential systems with delayed impulses is considered. By employing piecewise continuous Lyapunov functions and the Razumikhin techniques, several criteria on the exponential stability and uniform stability in terms of two measures for the mentioned systems are obtained, which show that unstable stochastic functional differential systems may be stabilized by appropriate delayed impulses. Based on the stability results, delayed impulsive controllers which mean square exponentially stabilize linear stochastic delay systems are proposed. Finally, numerical examples are given to verify the effectiveness and advantages of our results.