P-th Moment And Almost Sure Stability Of Impulsive Stochastic Nonlinear Systems With Delay

In recent years,stochastic system has become a hot issue in the field of system theory,and it has been widely used in chemistry,biology,economics,physics and any other fields.In the real systems,there always exist impulse and delay phenomena,and consider these factors can make a model more consistent with the actual systems.However,the impulsive and delay in the stochastic system may lead to the system unstable or stability becomes worse.Therefore,it is very important to study the stability of impulsive stochastic systems with delay.In this thesis,moment and pathwise stability of several classes of impul-sive stochastic nonlinear systems with delay have been investigated.According to Lyapunov stability theorem,we introduce a class of ?-type functions,and ex-tend p-th moment exponential stability and almost sure exponential stability of impulsive stochastic nonlinear systems with delay to the ?? stability.By using Burkholder-Davis-Gundy inequality,It(?) formula,Razumikhin method and oth-er technologies,p-th moment ?? stability and almost sure ?? stability of these several impulsive stochastic nonlinear systems with delay are obtained.In chapter 2,3,4,the stability of impulsive stochastic nonlinear sys-tems with delay,impulsive stochastic nonlinear delay systems with Markovian switching and neutral impulsive stochastic nonlinear systems with delay are in-vestigated.According to Razumikhin approach,some sufficient conditions are given and proved of these several class of systems respectively.In addition,the simulation examples demonstrate the effectiveness of obtained results.