Stability And Robustness Analysis Of Neutral Stochastic Delay Differential Equations

In this paper, we mainly consider the stability of two classes of neutral stochastic delay differential equations, one kind is exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching, the other is robustness analysis of global exponential stability of nonlinear stochastic systems with respect to neutral terms and time-varying delays. By spliting the large-scale system into several classes and lumping the states in each class into one class by the different states of changes of the subsystems; then, we give a limit system to effectively replace the large-scale system. Under suitable conditions, using the stability of the limit system as a bridge, the desired asymptotic properties of the large-scale system with Brownian motion and Poisson jump are obtained by utilizing perturbed Lyapunov function methods and Razumikhin-type criteria. At the same time, we study the robustness of global exponential stability of nonlinear stochastic systems subject to time-delay and neutral term by using a subtle inequality and solving a transcendental equation.In chapter 1, we first introduce the application of stochastic differential equations and nonlinear stochastic system, the development and current situation of the neutral stochastic delay differential equations, and then give the main contents and thoughts of this article.In chapter 2, by utilizing perturbed Lyapunov function methods and Razumikhin-type criteria, we prove exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching, and give the conditions of pth moment exponential stability and the corresponding example is given to illustrate the application of the conclusion of this chapter.In chapter 3, we study the exponential stability of neutral stochastic functional system with pure jump and give the conditions of pth moment exponential stability. Finally, the concrete example is given to demonstrate the conclusion of this chapter.In chapter 4, by using a subtle inequality and solving a transcendental equation, we study the robustness of global exponential stability of a class of nonlinear stochastic systems with respect to neutral terms and time-varying delays and a corollary is given. Finally, a numerical simulation example is given to verify the conclusion of this chapter.