Criterions For Asymptotic Stability Of Autonomous Systems And Robust Control For Uncertain Systems With Time-delays

In this paper, the method of Lyapunov function is employed to study the asymptotic stability of autonomous systems, and the robust stabilization of a class of uncertain nonlinear systems with delays is considered.The contents of this dissertation are divided into four parts. In part one, the background of the asymptotic stability theory of autonomous systems and the robust control theory of uncertain systems is summarized.In part two, the method of Lyapunov function is employed to study the asymptotic stability of autonomous systems, the equivalent condition and two new sufficient conditions of the asymptotic stability for the systems are given. The sufficient conditions are more general than Krasovskii-Barbasheen theorem,and more convenient to use than LaSalle invariance principle. Finally, an illustrative example is given to show the usefulness of the proposed sufficient conditions. In part three, the fuzzy optimal guaranteed cost control problem for a class of uncertain nonlinear system with time-varying input and multistate delays and a given quadratic cost function is considered. The Takagi-Sugeno (T-S) model with time-varying delays and parameter uncertainties is adopted for modeling of the nonlinear system. A sufficient condition for the existence of fuzzy guaranteed cost state feedback controller is presented in terms of the solvability to a certain system of linear matrix inequalities (LMIs), and the feasible solutions to the system of LMIs provide a parameterized representation of a set of fuzzy guaranteed cost controllers. Furthermore, the characterization of fuzzy guaranteed cost controllers is exploited to solve the fuzzy optimal guaranteed cost control problem. An example is given to demonstrate the effectiveness of the proposed techniques.In part four, the problem of the fuzzy H∞state feedback control for a class of uncertain nonlinear systems with input and multiple state delays is addressed in this paper. The Takagi-Sugeno (T-S) model with time-delay and parameter uncertainties is adopted for modeling of nonlinear system. The systematic design procedure for the fuzzy robust controller based on linear matrix inequality (LMI) is given. A sufficient condition is derived for the existence of fuzzy H∞state feedback controller such that the closed-loop system is asymptotically stable and the effect of the disturbance input on controlled output is reduced to a prescribed level. An example is given to demonstrate the effectiveness of the proposed method.