Stability analysis of impulsive stochastic delayed differential systems with unbounded delays

Abstract In this paper, the stability analysis for impulsive stochastic delayed differential equations with unbounded delays is considered by applying stochastic analysis techniques and average dwell time approach. A novel Razumikhin-type criterion of the p th moment exponential stability is derived for the related systems. The feature of the criterion shows that time-derivatives of the Lyapunov functions are allowed to be indefinite, even unbounded, which can loosen the constraints of the existing results. As a corollary, the criterion of the p th moment exponential stability for stochastic delayed differential equations with unbounded delays without impulsive effects is also obtained. Finally, some examples are given to illustrate the usefulness and significance of the theoretical results.