Fuzzy control of nonlinear continuous-time systems

Fuzzy control has proved to be a successful control method for many kinds of nonlinear systems. However, the question, "for a given nonlinear system is it possible to design a fuzzy control system to stabilize this nonlinear system?", has not been answered yet. In this paper we try to answer this question by proving some universal approximation theorem, stability theorem and universal fuzzy controller theorems for a class of nonlinear systems which can be represented by a set of linear systems on a set of local regions. Furthermore we propose a constructive procedure to obtain the fuzzy controllers for this class of nonlinear systems.