A new stability condition for fuzzy control systems by using equivalence class in set theory

This paper is concerned with the stability analysis for T-S fuzzy control systems. By exploiting the property of the structure of fuzzy inference engine, an equivalence relation on index set of the product of rule weights is defined. Further, a new class of stability analysis conditions is proposed by using the equivalence classes under the relation. In contrast to the existing results, the new conditions are with less conservatism and a lighter computational burden. Numerical examples are given to illustrate the effectiveness of the proposed methods.