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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.
Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on (Volume:42 , Issue: 4 )
Date of Publication: Aug. 2012