Stability Of Neutral Stochastic Systems With Time-delay

It is known that the practice systems often contain not only information of the past state but also information of the derivative of the past state. It is quite common that time delays, parameter uncertainties and the nonlinear exist inherently in many dynamic systems, which often lead to instability and poor performance. On the other hand, stochastic systems, particularly the It(o|^) type stochastic systems have found successful applications in many branches of science and engineering systems. Therefore, the stability study of neutral stochastic systems with time-delay will offer better theoretical basic and means for dealing with practice, so it has attracted more and more researchers.This dissertation deals with the problems of stability for several kinds of neutral stochastic systems with time-delay. Employing Lyapunov second method, constructing the proper Lyapunov functional, by use of It(o|^) formula, linear matrix inequality theory and stochastic Lyapunov stability theory, time delay-independent and time delay-dependent stability criterions of the systems are derived respectively. The stability criterions are all expressed in terms of linear matrix inequalities. The results can be solved easily by using LMI toolbox in Matlab. Numerical examples illustrate that the criterions expressed in this dissertation are effective. The main works as following:Firstly, stability for the linear neutral stochastic systems with time-delay is studied. The stochastic asymptotic stability criterions are given through associating with the improved matrix inequality. The time delay-independent stability criterion can be generalized to some broad area. To the time delay-dependent stability, it is given that the method of solving the maximum time delay. Secondly, based on the previous stochastic asymptotic stability criterions of the normal systems, the robust stochastic stability criterions for the uncertain neutral stochastic systems with time-delay are derived under the condition of the uncertainty structure with norm-bounded. Finally, the dissertation discusses the stability for a class of nonlinear neutral stochastic system with time-delay. It is given that the time delay-dependent sufficient condition of asymptotic stability in mean-square, which can be applied to derive the more simple stability criterion in the general time-delay system.