Stability Analysis Of A Class Of Neutral Delay Stochastic Differential Equations

With the application of stochastic time-delay systems in many fields,such as engineering,especially in the control theory,many scholars have begun to focus on the study of the stochastic systems with time-delays.For these systems,neutral stochastic differential equations are commonly used to describe the stability of the system by analyzing the stability of the solution.The problem of time-delay is ubiquitous in life,and it is the main factor that destabilizes the system,which make many scholars focus on the problem.Therefore,the research on neutral time-delay stochastic systems has become a hot topic.The paper based on the time-delay neutral stochastic linear system mainly studies the mean-square exponential stability of a class of neutral stochastic differential equations with multiple delays.Firstly,based on the analysis of the stability of the operator D,the paper obtains a sufficient condition by introducing the spectral radius condition,which less conservative to ensure that the operator's stability.This is used as the basis for the subsequent stability determination of the paper.At the same time,a new condition for determining the stability of the system equation was obtained.Further,a new Lyapunov-Krasovskii function is constructed for the system equations.It inclues all possible secondary integral functions and the number of inclusions is minimized,which reduces the conservation and computational complexity.Besides,the corresponding Lyapunov-Krasovskii functions are constructed for the different relation-ships between time-delay points.Afterwards,based on the new constructed Lyapunov-Krasovskii function,this paper obtains the sufficient conditions expressed by the linear matrix inequality for the exponential stability of the neutral stochastic stochastic system.Moreover,in the process of exploring stability,the corresponding Newton-Leibniz formulas are introduced for different time delay points.And once again,the conservativeness of sufficient conditions to ensure the stability of a neutral stochastic time-delay system is reduced,making the result more better.Finally,this paper analyzes the critical situation between time delays and gives the numerical examples to test the validity of the aforementioned conclusions and the effectiveness of approaches is illustrated...