T-S fuzzy systems approach to approximation and robust controller design for general nonlinear systems

A novel approach to control of general nonlinear system based on T-S fuzzy model is presented in this paper. Firstly, it is shown that a general nonlinear system can be approximated by a generalized T-S fuzzy model to arbitrary degree of accuracy on any compact set. And the basic idea of the proposed approach is to stabilize the general nonlinear system by solving a robust stabilization problem of the developed T-S fuzzy system with the approximation errors as the uncertainty term. Then using a piecewise Lyapunov function, robust semi-global stabilization and generalized H₂ control of the general nonlinear system are formulated in the form of linear matrix inequalities. Finally, an example is provided to demonstrate the effectiveness of the proposed approaches.