Stability Of Stochastic Impulsive Systems With Interval Time Delays

Time-delay and impulse is often encountered in various physical and engineering systems,such as communication systems,circuit systems,and biological systems.In addition,the system will inevitably be affected by uncertainties in practical applications,causing the system can not achieve the expected control requirements.Therefore,it is very significant to study stochastic impulsive systems with interval time delays.The property of stability is a very important of the dynamical system,and also stability studies are also the precondition of these engineering applications.Especially in recent years,the stability has attracted considerable attention.Hence,it's necessary to study the stability of stochastic impulsive systems with interval time delays.Based on Lyapunov functional method,stochastic analysis theory and linear inequality techniques,this paper investigates the stability of three systems,including interval time-delay stochastic system,stochastic system with interval time-delay and impulsive controller,a semi-linear stochastic differential system with switching and impulse.The main work of this paper is listed as follows:1.For a class of interval stochastic time-delay systems,an appropriate Lyapunov function is constructed.By using Ito differential equations and LMI methods,the time-delay dependent and delay independent criteria are established.Several examples illustrate the feasibility of the results of this chapter.And compared with previous work.2.On the basis of the work one,the stability of a class of non-linear stochastic system with interval time-delay and impulsive controller is studied.The new mean square is established by using Razumikhin technique,Lyapunov function,integral inequality and linear matrix inequality technique.Then the stochastic analysis technique is used to construct the inequality,and the mean square exponential stability condition of the system is generalized.Finally,some numerical examples are given to illustrate the validity of the proposed stability criterion.3.For a class of semi-linear stochastic differential system with switching and impulse,the global asymptotic mean-square stability and global p-th stability conditions are studied by constructing suitable Lyapunov functions and using Ito equations and impulsive differential inequalities.