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H∞ Takagi-Sugeno Fuzzy State-Derivative Feedback Control Design for Nonlinear Dynamic Systems

Authors: N. Kaewpraek, W. Assawinchaichote


This paper considers an H TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an HTS fuzzy state-derivative feedback control law which guarantees L2-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.

Keywords: H∞ fuzzy control, LMI, Takagi-Sugano (TS) fuzzy model, nonlinear dynamic systems, state-derivative feedback.

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[1] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. on Syst. Man, and Cybern., vol. SMC-15, 1985, pp. 116-132.
[2] S. K. Nguang and P. Shi, “ H∞ fuzzy output feedback control design for nonlinear systems: An LMI approach,” IEEE Trans. on Fuzzy Syst., vol. 11, 2003, pp. 331-340.
[3] W. Assawinchaichote, “A non-fragile H∞ output feedback controller for uncertain fuzzy dynamical systems with multiple time-scales,” Int. J. Computers, Communications & Control, vol. 7, 2012, pp. 8-19.
[4] W. Assawinchaichote and S. K. Nguang, “Fuzzy control design for singularly perturbed systems: An LMI approach,” Proc. ICAIET, (Kota Kinabalu, Malaysia), 2002, pp. 146-151.
[5] W. Assawinchaichote and S. K. Nguang, “ H∞ fuzzy control design for nonlinear singularly perturbed systems with pole placement constraints: An LMI approach,” IEEE Trans. on Syst. Man, and Cybern., vol. 34, 2004, pp. 579-588.
[6] W. Assawinchaichote, S. K. Nguang, P. Shi, and M. Mizumoto, “Robust H∞ control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach,” 43rd IEEE Conference on Decision and Control, 2004, pp. 803-808.
[7] S. K. Nguang, W. Assawinchaichote, P. Shi, and Y. Shi, “H∞ fuzzy filter design for uncertain nonlinear systems with Markovian jumps: an LMI approach,” Proceedings of the American Control Conference, 2005, pp. 1799-1804.
[8] S. K. Nguang, W. Assawinchaichote, and P. Shi, “H∞ filter for uncertain Markovian jump nonlinear systems: An LMI approach,” Int. J. Circuits Syst. Signal Process, vol. 26, 2007, pp. 853-874.
[9] W. Assawinchaichote, “A new robust H∞ fuzzy state-feedback control design for nonlinear Markovian jump systems with time-varying delay,” Control and Cybernetics, vol. 43, no. 2, 2014, pp. 227-248.
[10] W. Assawinchaichote, S. K. Nguang, and P. Shi, “H∞ fuzzy state feedback control design for nonlinear systems with D-stability constraints: An LMI approach,” ScienceDirect Maths. and Com. Sim., vol. 78, 2008, pp. 514-531.
[11] S. H. Kim and P. Park, “H∞ state-feedback-control design for discrete-time fuzzy systems using relaxation technique for parameterized LMI,” IEEE Trans. Fuzzy Syst. vol.18, no. 5, 2010, pp. 985-993.
[12] W. Assawinchaichote, “Synthesis of a robust H∞ fuzzy controller for uncertain non-linear dynamical systems,” in Fuzzy Controllers Theory and Applications ed. T. L.Grigorie Intech Press, Croatia, 2011, pp. 111-132.
[13] N. Kaewpraek and W. Assawinchaichote , “Control of PMSG wind energy conversion system with TS fuzzy state-feedback controller,” Applied Mechanics and Materials, vol. 446-447, 2014, pp. 728-732.
[14] W. Assawinchaichote, “Further results on robust fuzzy dynamic systems with D-stability constraints,” Int. J. Applied Mathematics and Computer Science, vol. 24, no. 4, 2014, pp. 785-794.
[15] H. Gassara, A. EI Hajjaji and M. Chaabane, “Observer-based robust H∞ reliable control for uncertain T-S fuzzy systems with state time delay,” IEEE Trans. Fuzzy Syst. vol.18, no.6, 2010 pp. 1027-1040.
[16] J. Luo, Y. Liu, Y. Dong and X. Min, “State-derivative-dependent robust H∞ controller design for T-S fuzzy time-delay systems,” IEEE Conference. Chinese cont. and Decision.,2010, pp. 311-316.
[17] H. Ghorbel, A. EI Hajjaji, M. Souissi and M. Chaabane, “Robust tracking control for Takagi-Sugeno fuzzy systems with unmeasurable premise variables: Application to tank system,” ASME Trans. Dyna. Syst., Measu., and Cont. vol.136, 2014, pp. 1-8.
[18] G. R. Duan and X. Zhang, “Regularizability of linear descriptor systems via output plus partial state derivative feedback”, Asian J. Control. Vol. 5, no. 3, 2003, pp. 334-340.
[19] T. H. S. Abdelaziz and M.Valas'ek, “Pole-placement for SISO linear systems by state-derivative feedback”, IEEE Proc. Contr. Theory Appl. vol. 151, no. 4, 2004, pp. 377-358.
[20] R. Cardim, M. C. M. Teixeira, E. Assuncao and F. A. Faria, “Control designs for linear systems using state-derivative feedback”, in Systems Structure and Control ed. P. Husek (InTech, Available form: ), 2008, pp. 1-28.
[21] F. Valenciaga, P. F. Puleston, and P. E. Battaiotto, “Power control of photovoltaic array in a hybrid electric generation system using sliding mode techniques,” IEE Proc. on Cont. Theory Appl., vol. 148, 2001, pp. 448-455.