Stability Analysis And Controller Design For Discrete T-S Fuzzy Control System

The stability and design of fuzzy control systems have been the most important problems in fuzzy theory. The research of fuzzy control theory includes a series of main problems, such as the stability analysis, the system design approaches and the improvement of the system performance. It is difficult of the stability for fuzzy control because of nonlinearity of fuzzy systems. There have existed a lot of measures to ensure the stability of fuzzy control systems. However the perfect theory system has not been formed. It is necessary to study the theoretical problems more deeply.With the T-S fuzzy model, which brings far-reaching impact for fuzzy control theory and its application, and makes stability analysis of fuzzy systems to a new theoretical height. Now, some results have been applied into practical systems. An advantage of a T-S fuzzy model is that it can fully use Lyapunov stability theory to analyze stability of systems and design controller, and a systematic method is provided to study the problem of stability of nonlinear systems and controller design by T-S fuzzy model ling for nonlinear systems. In this thesis, the controllers designed and stability analysis of T-S fuzzy control system are mainly discussed.The main contents are as follows:(1) Summarize the development of fuzzy control, adaptive fuzzy control, some methods of stability analysis, and the fuzzy controller's design; introduce the construction method of T-S fuzzy system model, and some methods of Lyapunov stability analysis; rewrite the system to be an equivalent discrete-time switching fuzzy system according to quadratic Lyapunov function, and then give an example to explain how we divide the state space into two kinds of subregions and why the switching fuzzy system is equivalent to the original system;(2) Propose a new relaxed stabilization criteria and a method of the state feedback controller's design for discrete-time T-S fuzzy system based on discrete-time switching fuzzy system, and then using numerical simulation to show that our criterion is more relaxed than the current criteria and the effectiveness of the fuzzy controller's design method; in the conclusion, the thesis indicates some unsolved problems and prospects of the further study.