A study on coincidence of symbolic and continuous behavior for symbolic stability analysis

Fuzzy inference has a multi-granular architecture consisting of symbols and continuous values, and this architecture has worked well to incorporate experts' know-how into fuzzy controls. Stability analysis is one of the main topics of fuzzy control. A stability analysis based on the symbolic expression of a fuzzy control system is proposed. This method is a good tool for the design of a stable fuzzy controller using symbols. This paper introduces a "chain of rules" to clarify the description of the behavior of fuzzy control systems. A coincidence of the symbolic and continuous behavior is defined. A sufficient condition together with a new inference method that guarantees the coincidence of symbolic and continuous behavior of fuzzy control systems is revisited.