Fuzzy control of nonlinear discrete-time systems

Fuzzy control has proved to be a successful design methodology for many kinds of nonlinear systems. The essential characteristics of fuzzy control are first analyzed in this paper. The fuzzy controller design methods can be considered as the local design methods. When a nonlinear system is given is it possible to design a fuzzy control system to stabilize this nonlinear system by the local design methods? In this paper we try to answer this question by proving some universal approximation theorems, stability theorems 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