Theoretical analysis of a fuzzy-logic controller with unequally spaced triangular membership functions

The mathematical analysis concerning the explicit input/output relation of the fuzzy logic controller (FLC) is addressed in this article. Under the as sumption of simple rule mapping and the use of arbitrarily located triangul ar fuzzy partitions as the membership functions, the inferred output of the FLC can be decomposed into two terms: the global multilevel relay and the local nonlinear compensator. The ultimate control behavior of this FLC and the equivalence to nonlinear proportional-integral (PI) controller, as the number of linguistic terms are approaching to infinity, are also investigat ed. The local stability criteria for PI-type FLCs are derived and the globa l stability properties for PD-type FLCs are established. This analysis is a generalization to previous related research works where the FLC is charact erized by equally spaced triangular fuzzy partitions on the universal sets. (C) 1999 Elsevier Science B.V. All rights reserved.