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

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5 Author(s)
Qing Gao ; Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong ; Xiao-Jun Zeng ; Gang Feng ; Yong Wang
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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.

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IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)  (Volume:42 ,  Issue: 4 )