Analysis and synthesis conditions for T-S fuzzy continuous-time systems with partially matched premises

A recognized challenge in the Takagi-Sugeno (T-S) fuzzy controller design concerns the use of different membership functions (MF) for controller and system. Most of the conditions available in the literature require that the controller’s MF matche the system’s one. Therefore, the implementation of such controllers may lead to unsafe operational conditions whenever such a match is lost. The main contribution of this paper is to provide new convex formulations for both stability analysis and controller design for T-S fuzzy systems under unmatched MF. We assume the same number of premises, yielding conditions called partially matched premises. To reduce conservatism, we use the Lyapunov approach, and we write the MF of the controller from the MF of the system. Two examples serve to compare our approach with others found in the literature. The achieved results suggest that our method outperforms the others.