Some criteria on exponential stability of impulsive stochastic functional differential equations

This paper is mainly concerned with p$$ p $$th moment exponential stability of impulsive stochastic functional differential equations. By using the Lyapunov direct method and mathematical induction, we obtain a new generalized impulsive Halanay inequality and some new criteria, which contain two scenarios regarding influence of impulses. On the one hand, when the system itself is unstable, a suitable unidirectional impulse or sequence of impulses can be added to make it stable. On the other hand, we discuss how much impulse perturbation the system can withstand without destabilizing the original system. Finally, two examples are illustrated to show the validity and universality of our results.