Another Multiple Lyapunov Function Approach to Stabilization of Fuzzy Systems

The paper presents results on stability analysis and controller synthesis of Takagi-Sugeno (T-S) fuzzy systems. A T-S fuzzy model is known to be usable in modeling and control of a wide range of nonlinear systems. In the paper, the multiple Lyapunov functions method is applied to formulate a sufficient condition for the stability of a T-S fuzzy system. Unlike previous approaches, the paper adopts an assumption on the time-derivatives of membership functions that better reflects the activation of fuzzy rules. The stability criterion is established in terms of linear matrix inequalities (LMIs). These LMIs differ from existing ones by explicitly considering the role of the membership functions on governing the negative definiteness of the derivative of the Lyapunov function candidate. Controller design methods are also stated in terms of matrix inequalities. The stability analysis and controller design methods are illustrated in terms of simulation examples.