An Approach to Fuzzy Control for a Class of Nonlinear Systems: Stability and Design Issues

Abstract

In order to ensure the stability of a fuzzy control system for a class of nonlinear systems, a stability criterion is derived from Lyapunov’s direct method. In this article, instead of linearizing the nonlinear system around several operating points and using a T-S fuzzy model to represent the plant, the authors use the technique of feedback linearization as a part of the control action on the consequent (conclusion) parts of the fuzzy rules. So, linear system in a new coordinate will be generated associated with each fuzzy subsystem, and if these linear systems are stable under common Lyapunov function, then the corresponding nonlinear system is stable. Based on the stability criterion, a fuzzy logic controller design method will be proposed. The proposed design acts as multivariables state feedback in order to stabilize the nonlinear system in systematic manner. Finally, a numerical example is given to illustrate the concept of the proposed controller with comparison with state feedback controller.