T–S-Fuzzy-Model-Based Approximation and Controller Design for General Nonlinear Systems

This paper presents a novel approach to control general nonlinear systems based on Takagi-Sugeno (T-S) fuzzy dynamic models. It is first shown that a general nonlinear system can be approximated by a generalized T-S fuzzy model to any degree of accuracy on any compact set. It is then shown that the stabilization problem of the general nonlinear system can be solved as a robust stabilization problem of the developed T-S fuzzy system with the approximation errors as the uncertainty term. Based on a piecewise quadratic Lyapunov function, the robust semiglobal stabilization and H_∞ control of the general nonlinear system are formulated in the form of linear matrix inequalities. Simulation results are provided to illustrate the effectiveness of the proposed approaches.

I. Introduction

In RECENT decades, control methodologies based on the Takagi–Sugeno (T-S)-type dynamic fuzzy model [1] have attracted great attention from the control community. There have been many successful applications of T-S-fuzzy-model-based approaches to complex nonlinear system control [2]–[8]. A T-S fuzzy model describes a nonlinear system by a group of fuzzy IF–THEN rules in the form of local linear or affine models which are smoothly connected by fuzzy membership functions. This structure provides a basis for the systematic stability analysis and controller design of T-S fuzzy control systems in view of powerful conventional control theory.