Fuzzy Control System Design via Fuzzy Lyapunov Functions

This correspondence deals with the problems of analysis and design for a class of continuous-time Takagi-Sugeno fuzzy control systems. Sufficient conditions for the stability of fuzzy control systems are derived based on a fuzzy Lyapunov function. Both parallel and nonparallel distributed compensation controllers are considered. Sufficient conditions for the solvability of the controller design problem are given in the form of linear matrix inequalities. Unlike the fuzzy Lyapunov function approaches reported in the literature, the bound of the time derivatives of the fuzzy basis functions is not required in the proposed approaches. The effectiveness of the proposed approaches is shown through a numerical example.