Exponential stability of stochastic differential delay systems with delayed impulse effects

In this paper, we investigate the stability of stochastic delay differential systems with delayed impulses by Razumikhin methods. Some criteria on the pth moment exponential stability are obtained. It is shown that if a stochastic delay differential system is exponentially stable, then under some conditions, its stability is robust or weaken with respect to delayed impulses. Moreover, it is also shown that an unstable stochastic delay system can be successfully stabilized by delayed impulses. The effectiveness of the proposed results is illustrated by three examples.