Fuzzy inference has a multigranular architecture consisting of symbols and continuous values, and has worked well to incorporate experts' know-how into fuzzy controls. Stability analysis of fuzzy control systems is one of the main topics of fuzzy control. A recently proposed stability analysis method on the symbolic level opened the door to the design of stable fuzzy controller using symbols. However the validity of the stability analysis in the symbolic system is not guaranteed in the continuous system. To guarantee this validity, a nonseparate condition has been introduced. If the fuzzy control system is asymptotically stable in the symbolic system and the system satisfies the nonseparate condition, the continuous system is also asymptotically stable. However this condition is too conservative. The new condition called a relaxed nonseparate condition has been proposed and the class of control systems with guaranteed discretization has been expanded. However the relaxed condition has been applicable only to controf systems having symmetric membership functions. This paper presents a new fuzzy inference method that makes the relaxed condition applicable to fuzzy control systems with asymmetric membership functions. Simulations are done to demonstrate the effectiveness of the new fuzzy inference method. The proof of the expansion of the relaxed nonseparate condition is also given.
Stability analysis for a class of Takagi–Sugeno fuzzy control systems with PID controllers
