An approach to synthesis and approximation of stable fuzzy logic controllers

This paper studies the method for synthesizing stable fuzzy controllers and the approximation in terms of Mamdani model to stabilize nonlinear systems. A stability criterion for determining the feedback control coefficients is given based on Takagi-Sugeno model. It is shown that by suitably partitioning the universe of discourse of the output membership functions, the defuzzified function surface can have at most limited number of points equal to those of a given surface. This result is then used to approximate a controller via Mamdani model and an algorithm for deriving such a stable fuzzy logic controller is detailed. An inverted pendulum is taken as example to demonstrate the methodology developed in this paper.