An approach to fuzzy control of nonlinear systems: Stability and design issues

We present a design methodology for stabilization of a class of nonlinear systems. First, we represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called ''parallel distributed compensation'' is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMI's. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart.