Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching

This paper investigates the stability analysis and performance design of nonlinear systems. To facilitate the stability analysis, the Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear plant. Under the imperfect premise matching in which T-S fuzzy model and fuzzy controller do not share the same membership functions, a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant. However, the nice characteristic given by the perfect premise matching, leading to conservative stability conditions, vanishes. In this paper, under the imperfect premise matching, information of membership functions of the fuzzy model and controller are considered in stability analysis. With the introduction of slack matrices, relaxed linear matrix inequality (LMI)-based stability conditions are derived using Lyapunov-based approach. Furthermore, LMI-based performance conditions are provided to guarantee system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.