Structure analysis and system design for a class of Mamdani fuzzy controllers

Analytical analysis of the structure of fuzzy controllers is important as it provides insightful information and makes it possible to eliminate or reduce the trial-and-error effort in system design. Most results available in the literature only deal with the fuzzy controllers using up to three input variables (i.e. PI, PD, or PID type with the input space being three dimensional at most). In this paper, we study a class of Mamdani fuzzy controllers whose input space can be arbitrary dimension. We derived mathematically the input-output relation for these fuzzy controllers. We also investigated the bounded-input bounded-output global stability as well as local stability of the fuzzy control systems. Based on the explicit input-output relation and the local stability property, a procedure for designing the fuzzy controllers regulating (nonlinear) plants is proposed. Its effectiveness is demonstrated by a numerical example with computer simulations.