An LMI-based stable fuzzy control of nonlinear systems and its application to control of chaos

We present a systematic framework for the stability and design of nonlinear fuzzy control systems. First we represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of 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 LMIs. The design methodology is illustrated by application to the problem of modeling and control of a chaotic system-Chua´s circuit