On Input-to-state Stability Of Neutral Stochastic Functional Differential Equations

In this paper, we discuss the input-to-state stability of neutral stochastic functionaldifferential equations.Using Lyapunov function and Razumikhin techique, we gets thecriteria of ISS on the pth moment of neutral stochastic differential equations. Thesecorresponding results obtained recently are improved. Finally, an example is discussedto illustrate the theorem.First of all in the introduction section, we introduce the twosystems and the relevant research background, which makes us to know more about theproblem. Meanwhile, we also elaborate some basic knowledge in this section, whichmakes preparations for the next research.In the first chapter,the introduction is devoted to a study on the researchprogrammes as well as used in this paper,and the paper gives a simple description of thesymbols and basic definitions.At last, we give the main conclusion of this paper and thestructured of the paper.In the second chapter,we use the Lyapunov functions and Razumikhin techique inthe neutral stochastic differential equation, taking into account the input-to-statestability (ISS), and estabilishing the new Razumikhin theory of the pth momentinput-to-state stability in neutral stochastic differential equation. Then we give theappropriate example to illustrate the theorems.Finally, in the third chapter, on the basis of second chapter, we study theinput-to-state stability in Neutral stochastic differential equation with the Markovswitching, and estabilish the new Razumikhin theory of the pth moment input-to-statestability in neutral stochastic differential equation with the Markov switching.Finally,we give the appropriate example to illustrate the theorems.