| Fuzzy control is an advanced control theory based on fuzzy set theory, fuzzy language variables and fuzzy logic consequence. As a main branch of intelligent control, fuzzy control has been attained many greatness achievements no matter in the field of theory or applications. Therefore fuzzy control is going to be considered as one of the most important technology in the field of research and application for the future. In the control field, fuzzy systems are used as a nonlinear function approximation tool. In 1985, both Takagi and Sugeno proposed the Takagi-Sugeno (T-S) fuzzy model, which bring far-reaching impact for fuzzy control theory and its application, and makes stability analysis of fuzzy system to a new theoretical height. Now, some results have been applied into practical system. An advantage of a T-S fuzzy model is that it can use Lyapunov stability theory to analyze stability of systems and design controller, and a system and controller design by T-S fuzzy modeling for nonlinear systems.The stability analysis and design of fuzzy control systems have been the most important problems in fuzzy theory, but it is difficult to analyze the fuzzy control systems as it is nonlinearity. Up to now, there have existed a lot of measures to ensure the stability of fuzzy systems; The perfect theory has not formed yet. It is necessary to study these problems more deeply.This paper focus on the study of the stability of T-S fuzzy systems, and some innovation in the theory are obtained, which is benefit to providing new thoughts and new methods for the study of T-S fuzzy systems.In Chapter1, the present research situation and development of fuzzy control theory are summarized. Then a brief analysis of the basic idea of fuzzy control theory. Finally, the development of fuzzy control theory and technology in and abroad are summarized. In Chapter2, we mainly introduced basic theories and relevant concept of fuzzy control system, but also describes the stability analysis of fuzzy control system research methods. This elementary knowledge has provided certain rationale for this article research work.In Chapter3, frist systematically introduce the method of set up T-S fuzzy model which is accused of the target, also discussed stability criteria of the controlled object as a T-S fuzzy model. Then the stability of T-S fuzzy model for continuous-time and discrete-time are proposed. Finally, sufficient condition of T-S fuzzy model for closed-loop and open-loop are obtained.In Chapter4,based on piecewise fuzzy Lyapunov function that proposed by Feng,Johnsson,Ren and others, the properties of fuzzy control systems employing two-overlapped fuzzy partition inputs are studied. According to these a new sufficient condition for the stability of a T-S fuzzy control system is proposed. It can reduce the conservation and difficulty of former stability analysis methods. Finally, an example shows that our method is more effective.
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