Stability Conditions and Control Designs via Improved Lyapunov Function for Takagi-Sugeno Fuzzy Descriptor Systems

This paper is concerned with control design methods via a new Lyapunov function for fuzzy descriptor systems. Takagi-Sugeno fuzzy descriptor model, that can represent nonlinear systems, are divided into two families: one with same membership functions in both sides of fuzzy systems and another with different membership functions in right and left side of fuzzy systems. Although many papers propose control designs for the above two systems that are derived from Lyapunov stability theory, they are very conservative because they use a Lyapunov function including a single Lyapunov matrix. In this paper, to design less conservative conditions, we propose new Lyapunov functions with all Lyapunov matrices that are multiple. Finally, numerical examples are given to show the effectiveness of our methods.