Analysis And Design For A Class Of Stochastic Continuous Nonlinear Systems

This dissertation mainly discusses the problems of stability analysis and controller synthesis fora class of stochastic continuous nonlinear systems. In general, these systems contain some factors,such as parameter uncertainty, time-varying delays, random disturbance, which is closer to the actualcomplex system model. It is of important theoretical and application value to research this kind ofsystem. The main results obtained in this thesis can be described as the following three parts:Part1: The problems of robust stability and stabilization for a class of stochastic systems withuncertain time-varying delay and parameter uncertainty are discussed in this part. First of all, a time-delay dependent Lyapunov-Krasovskii functional is constructed by using a kind of general time-delaydecomposition techniques. Then the sufficiency conditions of robust stochastic stability are derivedwhich based on Lyapunov stability theory, Ito differential formula and convex combination matrixinequality technique. In addition, based on these stability conditions obtained, a desired controllercan be designed to guarantee the stability of the corresponding closed-loop systems. Finally, twonumerical examples are given to illustrate the effectiveness of the methods proposed.Part2: This part is concerned with the stability and stabilization problems of T-S fuzzy stochasticsystems with time-varying delays. Lyapunov-Krasovskii functional is constructed by using delaydecomposition approach. And based on Lyapunov stability theory, the Ito formula, Schur complementlemma and isometry property, the delay-dependent stability criterions in the mean square are derivedfor nonlinear delayde stochastic systems. Then employing these results obtained, a state feedbackcontroller can be constructed. A numerical example is given to verify the effectiveness of the designapproaches.Part3: In this part, we considered the problems of robust stochastic stability and stabilization fora class of T-S fuzzy stochastic systems with parameter uncertainty. The considered systems containWiener process and parameter uncertainty with linear fractional structure. A matrix decompositionapproach has to be used to analyze the stability of systems, and then established the sufficiencyconditions of robust stochastic stability. Meanwhile, a desired controller is given to guaranteethe stability of the closed-loop systems based on the sufficiency conditions obtained. Finally the simulation examples are given to show the effectiveness of the proposed design method.