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Application and robustness design of fuzzy controller for resonant and chaotic systems with external disturbance. (English) Zbl 1137.93371

Summary: A robustness design of fuzzy control via model-based approach is proposed in this paper to overcome the effect of approximation error between nonlinear system and Takagi-Sugeno (T-S) fuzzy model. T-S fuzz model is used to model the resonant and chaotic systems and the parallel distributed compensation (PDC) is employed to determine structures of fuzzy controllers. Linear matrix inequality (LMI) based design problems are utilized to find common definite matrices \(P\) and feedback gains \(K\) satisfying stability conditions derived in terms of Lyapunov direct method. Finally, the effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic and resonant systems.

MSC:

93C42 Fuzzy control/observation systems
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References:

[1] Khalil H. K., Nonlinear Systems (1992) · Zbl 0969.34001
[2] Zadeh L., IEEE Trans. Syst., Man, Cybern. 3 pp 28–
[3] Mohammad R. E., IEEE Trans. Fuzzy Syst. 6 pp 346–
[4] DOI: 10.1109/3477.740162 · doi:10.1109/3477.740162
[5] DOI: 10.1109/91.481841 · doi:10.1109/91.481841
[6] DOI: 10.1109/91.481840 · doi:10.1109/91.481840
[7] Yeh K., Int. J. Uncertainty, Fuzziness and Knowledge-Based System. 3 pp 255–
[8] Ma X. J., IEEE Trans. Fuzzy Syst. 6 pp 41–
[9] DOI: 10.1109/91.728444 · doi:10.1109/91.728444
[10] DOI: 10.1109/91.797980 · doi:10.1109/91.797980
[11] Lee H. J., IEEE Trans. Fuzzy Syst. 9 pp 369– · doi:10.1109/91.919258
[12] Clough R. W., Dynamics of Structures (1993)
[13] Joo Y.-H., IEEE Trans. Fuzzy Syst. 7 pp 394–
[14] Takagi T., IEEE Trans. Syst., Man, Cybern. 15 pp 116–
[15] DOI: 10.1137/1.9781611970777 · Zbl 0816.93004 · doi:10.1137/1.9781611970777
[16] DOI: 10.1016/0167-6911(88)90034-5 · Zbl 0634.93066 · doi:10.1016/0167-6911(88)90034-5
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