Stability Analysis And Research Of Impulsive Stochastic Differential Systems

Stability is an important index in system control,which is directly related to the performance of the system.At present,the research on the stability of control system is gradually increasing,which involves many majors and disciplines,including matrix theory and computer.In the long-term research,many practical results have been obtained and applied to the fields of communication and finance.However,due to the influence of noise and other factors,it is often difficult to maintain high stability during system operation.Therefore,the research on the influence of such factors has gradually become a hot topic in the stability analysis of control systems,especially the influence of random noise factors.On the other hand,when the transmission speed of the impulsive system is limited and the channel bandwidth is different,the time delay phenomenon will occur in the process of information transmission.This time delay usually exists in the impulsive part of the system.The research of stochastic differential systems with time-delay impulses has attracted more and more attention of many scholars,which has attracted the attention and participation of many researchers,and has obtained a lot of results,and has been gradually applied to the stability analysis and control of the system.This paper will focus on the exponential stability of impulsive stochastic differential systems.The main work includes the following three aspects:1、Almost sure exponential stability of impulsive stochastic differential systemsBy using the average dwell time(ADT)and Lyapunov function method,combined with Schur complement lemma,exponential martingale inequality and average impulsive interval,a class of two-dimensional impulsive stochastic differential systems is considered.The effective conditions for almost sure exponential stability of the system are obtained,and the existence and uniqueness of the general solution of almost sure exponential stability of the system are proved.Then,on this basis,a simple numerical example is used to verify the almost sure exponential stability of the two-dimensional impulsive stochastic differential system.Finally,the simulation results show that the proposed conditions are effective and correct.2、Almost sure exponential stability of delayed impulsive stochastic differential systemsThe stability problem of impulsive stochastic differential systems with time delay effect is studied.Firstly,the Lyapunov function is constructed,and the important theorem of almost sure exponential stability of impulsive stochastic differential systems with delay effect is obtained.In this process,the ?Ito calculus formula and stochastic analysis techniques are used.Then,through rigorous mathematical derivation and proof,the correctness of the proposed theorem is demonstrated.Finally,the validity and correctness of almost sure exponential stability are further verified by numerical examples and simulation analysis.3、P-th moment uniform exponential stability of delayed impulsive stochastic differential systems.The problem of p-th moment uniform exponential stability for delayed impulsive stochastic differential systems is studied by using stochastic analysis technique and average impulsive time method.A new p-th moment exponential stability criterion is proposed for related systems.Then,through mathematical derivation and proof,the correctness of the proposed criterion is demonstrated.Finally,numerical examples and simulation results show the effectiveness of the proposed p-th moment uniform exponential stability theory.