Stability Analysis Of A Class Of Neutral Stochastic Functional Differential Equations

Stochastic differential systems play an important role in many fields, such as economy, finance, physics, biology, medicine and so on. Therefore the theory of stochastic differential systems has developed rapidly in recent years. Particularly,the stability of stochastic differential systems has received considerable attention,such as p moment exponential stability and almost sure exponential stability. It is well known that stability is an important indicator for measuring the performmance of a stochastic system. Thus, stability is one of its main contents for a stochastic delay system. In addition, since there are some random disturbances in practical problems. So, whether from theoretical or from practical terms, the stability analysis of stochastic delay systems has a very important significance.In this paper, we will study stability of a class of neutral stochastic differential systems with time-delays, the considered system includes two kind of equations which are discussed respectively in the present paper. Firstly, an important conclusion about the property of the solution of neutral stochastic differential equations will be given before stability analysis and this conclusion will play an important role in the stability analysis of such systems. Secondly, analyzing the stability of these two kinds of neutral stochastic differential systems with two different time-delays, a suitable Lyapunov-Krasovskii functional will be constructed according to the Lyapunov stability theorem, and then a sufficient condition which is based on a linear matrix inequality(LMI) and can ensure the mean square exponential stability and almost sure exponential stability of the both stochastic systems will be presented. In the process of establishing sufficient conditions, we will also use Newton-Leibniz formula and basic principles of ?Ito calculus to introduce a slack variable in the LMI in order to reduce the conservative of the result we obtained. Finally, in the simulation section, four numerical examples are given to verify deeply the effectiveness and superiority of the results we obtained.