The Stability Analysis And Stochastic Stabilization For Neutral Stochastic Time-delay Systems

In the industrial systems, social economy, ecological engineering and otherfields, we often use the differential equations to describe the dynamic laws. Becauseof the random phenomenon, noise disturbance, and the uncertainty in the actualcontrol systems, we often use the stochastic differential equation to establish model.On the other hand, in the networked control systems, the process of metallurgicalindustry, aerospace systems and so on, there often exist time-delay phenomena.Therefore, the stochastic delay differential equations become a hot issue in thecontrol systems.Based on the functional differential equation and stochastic Lyapunov stabilitytheory, It differential formula, Schur lemma, and the method of linear matrixinequality (LMI), this thesis studies the stability and stochastic stabilization problemfor the neutral stochastic time-delay systems. The main results in this thesis areobtained as follows:1.The delay-dependent stability for the linear neutral stochastic time-delaysystems is discussed. We obtain the sufficient conditions by construct the properLyapunov function.2.The stabilization problem of neutral stochastic time-delay systems isinvestigated. The memory state feedback controller is designed. The problem ofH control problem for neutral stochastic time-delay systems is taken intoconsideration.3.For a class of nonlinear neutral stochastic time-delay systems, we use theGFL(Generalized Finsler lemma), and obtain the delay-dependent sufficientconditions for the stability. The method feasibility is proved through the numericalexample.