Symbolic stability analysis under relaxed non-separate condition with new fuzzy inference method

Stability analysis of fuzzy control systems is one of the main topics of fuzzy control. Previously, a stability analysis method on a symbolic level has been proposed. This method opened the door to the design of a stable fuzzy controller using symbols. The validity of the stability analysis in the symbolic system is not guaranteed in the continuous system. To guarantee this validity, a "relaxed non-separate condition" has been proposed. The problem is that this relaxed condition is only applicable to the systems that have symmetric membership functions. This paper introduces a new fuzzy inference method that enables us to use asymmetric membership functions under the relaxed condition. The proof of the related condition with the new fuzzy inference method is given in this paper.