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.