Stability Analysis And Application Of Stochastic Delay Systems With Delayed Impulses

This paper mainly studies the stability of stochastic delay systems with delayed impulses and the exponential synchronization of complex networks with time delays via delayed impulses.Based on the Lyapunov function,Razumikhin technique,linear matrix inequality tools and some random analysis techniques,some sufficient conditions for the mean square exponential stability of stochastic delay systems and a series of theorems for exponential synchronization of stochastic complex networks with time delays via delayed impulses are established.This article mainly studies the following contents:1.Investigates the stability of linear stochastic delay systems with delayed impulses.Based on the Lyapunov function and Razumikhin technique,some sufficient conditions for the mean square exponential stability of linear stochastic delay systems with stabilizing impulses or destabilizing impulses are established respectively.Then,on the basis of stability research,the problem of delayed impulse stabilization of stochastic delay systems is studied.Finally,two numerical examples are given to demonstrate the effectiveness of the results.2.Study the exponential synchronization problem of stochastic complex networks with time delay via delayed impulses.Based on the Lyapunov function method and linear matrix inequality tools,the sufficient conditions for exponential synchronization are established by using distributed impulses.And when the impulse controller degenerates into the effect of exponential synchronization can still be achieved even with complete delayed impulses.Finally,a numerical example is used to verify the validity of the results.