A New Limit Equation Based Stability Analysis of Linguistic Fuzzy Control System

Fuzzy control has always been an active discipline in fuzzy set theories and in fuzzy control the stability analysis is one of the most important issues and is also of great interest to scholars in this area. Many important results have been obtained in Tanaka-Sugeno fuzzy control system based on Lyapunov stability theory in the past ten years. Stability analysis in Mamdani fuzzy control system is still quite limited, though it is the first fuzzy controller of their kinds in literature. In this paper, stability analysis of Mamdani type fuzzy controller is studied based on a limit relation equation deduced from the generalized fuzzy control system. The structure and the solutions of the limit equation are closely related with the stability of the fuzzy system. The minimal solutions of the limit equation produce elementary stable matrix forms, which are useful to analyze the stability of closed loop fuzzy systems. An example from the level control of water tank illustrates the proposed method