New criteria on pth moment exponential stability of stochastic delayed differential systems subject to average-delay impulses

This note develops new stability criteria for stochastic delayed differential systems with average-delay impulses by using Razumikhin approach, stochastic analysis technique, average impulsive delay (AID) condition and average dwell time. Our results show that delayed system with destabilizing delaydependent impulses is pth moment exponentially stable, where delays in impulses can be flexible enough compared with some recent works. The feature of the criteria is that the Razumikhin function is allowed to be a time-varying and sign-changing function, which looses some restrictions of the existing results. Furthermore, a numerical example is performed to account for the effectiveness and the correctness of our theory.

Automated summary

This note presents new stability criteria for stochastic delayed differential systems with average-delay impulses. The results show that systems with destabilizing delay-dependent impulses are stable, even with flexible delays in the impulses.