Stability Analysis And Design For A Class Of T-S Fuzzy Control Systems

The stability analysis 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 system performance. It is difficult to study the stability of fuzzy control systems because its inner nonlinearity. Up to now, 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.This paper aims at the thorough research on the stability of fuzzy systems, and some innovations in the theory are obtained, which if of benefit to providing new thoughts and new methods for the investigation into fuzzy systems. Based on previous research, this paper deals with the stability analysis and stabilization of a class of Takagi-Sugeno (T-S) fuzzy systems via piecewise fuzzy Lyapunov function approach. In general, when an input gets into the rule base of fuzzy system, only partial rules are fired. Those unfired rules are not necessary to be considered for the local stability. In order employ this property in stability analysis, we divide the global fuzzy region into a set of un-overlap subregions, and analyze the stability based on fuzzy Lyapunov function. In the last, a controller based on parallel distributed compensation (PDC) and linear matrix inequality (LMI) is designed to stabilize the T-S fuzzy system.First, this paper summarizes the development of fuzzy control systems. And then, the method of the stability analysis of continuous and discrete T-S fuzzy control systems is expatiated in this paper, the stability conditions with less conservation of T-S fuzzy control systems are given on the basis of Lyapunov theory. Finally, using the methods of parallel distributed compensation (PDC) and linear matrix inequality (LMI), the stability analysis and design of T-S fuzzy control systems are investigated further, and corresponding results are given in LMIs.