T-S fuzzy systems approach to approximation and robust controller design for general nonlinear systems
Qing Zhong Gao, Gang Feng, Xiao‐Jun Zeng, Wang Yong · 2011
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 H2control 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.