Novel Stabilization Criteria for T–S Fuzzy Systems With Affine Matched Membership Functions

This paper presents a new parallel distributed compensation controller design approach for T–S (Takagi–Sugeno) fuzzy control systems with affine matched membership functions in the system and controller. In the new fuzzy control, affine transformed membership functions are adopted by scaling and biasing the original membership functions of the system. Stabilization and performance criterion of the closed-loop T–S fuzzy systems are obtained through a new parameterized linear matrix inequality, which is rearranged by affine matched membership functions. The conservativeness of stabilization condition for the T–S fuzzy system is significantly relaxed by utilizing the constraints condition of the controllers membership functions, which is determined from the difference of each transformed membership function. In addition, the controller gain is reconstructed by a decision variable separation technique with two different free weighting matrices without any scaling parameter. The superiority of proposed method is verified through numerical examples.