New Criteria on Input-to-State Stability for Stochastic Nonlinear Delayed Systems With Multiple Impulses

This article is committed to investigate the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i>th moment input-to-state stability for stochastic nonlinear delayed systems involving multiple impulses. Via a series of auxiliary equations, Razumikhin method and stochastic analysis approach, we derive some new stability results under the combination of impulsive control and impulsive disturbance. For all we know, this article is the first attempt to study such a stability issue for the suggested systems. Additionally, the concepts of stabilizing impulse average dwell time (SIADT) and destabilizing impulse average dwell time (DIADT) are proposed, respectively, owing to the presence of multiple impulses. It should also be pointed out that the obtained criteria can loose some restrictions of the existing results and have wider applications. Particularly, we allow the cumulative strength of multiple impulses over a period to be greater than 1, which is more applicable to some extent compared with most of the existing literatures. Finally, the effectiveness and validity of the theory are supported by two examples.