L₂-stabilization design for fuzzy control systems

System's stability is the most important requirement in control system designs. Fuzzy control system (FCS) should satisfy this requirement also. This paper shows that a linear plant with the formulated Fuzzy Logic Controller (FLC) is a nonlinear system and its stability can be analyzed by applying the Small Gain Theorem or the Circle Criterion. By these two criteria, three FLC design procedures are introduced to guarantee the stabilization of the FCS. Finally, two examples are given to confirm the availability of the proposed design approaches.