A design method of stable fuzzy controller on symbolic level based on relaxed non-separate condition

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. Earlier the stability analysis method on symbolic level has been proposed. This method was useful to grasp the behavior of fuzzy control systems, but sacrifices the rigorous analysis. In this method, the validity of the stability analysis on a symbolic level was not guaranteed in the continuous system. To guarantee this validity, a "non-separate" condition has been introduced. If the fuzzy control system is asymptotically stable in the symbolic system and the system satisfies the non-separate condition, the continuous system is also asymptotically stable. However this condition is too conservative. The paper introduces a new condition obtained by relaxing the non-separate condition. This new condition is called the "relaxed non-separate condition". The relaxed condition expands the class of fuzzy control systems with guaranteed granularization. The paper proposes a design method of an asymptotically stable fuzzy controller under the relaxed condition. Simulations are done to show the feasibility of the proposed design method.