p-Moment Stability of Stochastic Differential Delay Systems with Impulsive Jump and Markovian Switching

Abstract

This paper investigatesp-moment stability of the stochastic differential delay systems with impulsive jump and Markovian switching. Some stability criteria are obtained based on Lyapunov functional method and stochastic theory. It is shown that, even if all the subsystems governing the continuous dynamics without impulse are not stable, as impulsive and switching signal satisfies a dwell-time upper bound condition, impulses can stabilize the systems in thep-moment stability sense. The opposite situation is also developed for which all the subsystems governing the continuous dynamics arep-moment stable. The results can be easily applied to stochastic systems with arbitrarily large delays. The efficiency of the proposed results is illustrated by two numerical examples.