A new sufficient condition for stable fuzzy control system and its design method

Fuzzy inference has a multigranular architecture consisting of symbols and continuous values, and this architecture has worked well to incorporate experts´ know-how into fuzzy controls. The paper focuses on the important characteristic of fuzzy control, “symbolic expression” of a fuzzy control system. The paper first introduces a “chain of rules” to clarify the description of the behavior of the control systems. A coincidence of the symbolic and continuous behaviors is defined. With these definitions, the paper proposes a new condition, “relaxed nonseparate condition” and a new fuzzy inference method. The relaxed condition together with the new inference method guarantees the coincidence of symbolic and continuous behavior of the control system. The paper proposes a new design method of fuzzy controller that guarantees this coincidence. Simulations are done to show the feasibility of the relaxed nonseparate condition and proposed design method