Análise de estabilidade e síntese de controladores para sistemas fuzzy T-S discretos no tempo com premissas parcialmente combinadas

Abstract

This work proposes a relaxation that results in better stability analysis and controller synthesis for discrete-time Takagi-Sugeno (T-S) fuzzy systems subject to partially matched assumptions. This case, in which the controller and system have the same number of rules but differ in the parameters, is a frequent case in control applications, which has a great practical interest. The proposed approach is based on representing the error between two membership functions (MFs) through a second-order polynomial. The conditions are proposed as convex optimization procedures formulated as linear matrix inequalities (LMIs), guaranteeing efficient numerical solutions. Two examples illustrate the proposal; where the first one compares the proposed analysis condition with one found in the literature. The second example uses the synthesis condition to guarantee the stability of the closed-loop system, and the T-S fuzzy controller has membership functions different from the T-S fuzzy system. The results achieved suggest the superiority of the proposed method.