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

Authors: N. Kaewpraek; W. Assawinchaichote;

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

Abstract

{"references": ["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.", "S. K. Nguang and P. Shi, \" H\u221e fuzzy output feedback control design for nonlinear systems: An LMI approach,\" IEEE Trans. on Fuzzy Syst., vol. 11, 2003, pp. 331-340.", "W. Assawinchaichote, \"A non-fragile H\u221e output feedback controller for uncertain fuzzy dynamical systems with multiple time-scales,\" Int. J. Computers, Communications & Control, vol. 7, 2012, pp. 8-19.", "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.", "W. Assawinchaichote and S. K. Nguang, \" H\u221e 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.", "W. Assawinchaichote, S. K. Nguang, P. Shi, and M. Mizumoto, \"Robust H\u221e control design for fuzzy singularly perturbed systems with Markovian jumps: an LMI approach,\" 43rd IEEE Conference on Decision and Control, 2004, pp. 803-808.", "S. K. Nguang, W. Assawinchaichote, P. Shi, and Y. Shi, \"H\u221e fuzzy filter design for uncertain nonlinear systems with Markovian jumps: an LMI approach,\" Proceedings of the American Control Conference, 2005, pp. 1799-1804.", "S. K. Nguang, W. Assawinchaichote, and P. Shi, \"H\u221e filter for uncertain Markovian jump nonlinear systems: An LMI approach,\" Int. J. Circuits Syst. Signal Process, vol. 26, 2007, pp. 853-874.", "W. Assawinchaichote, \"A new robust H\u221e 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.\n[10]\tW. Assawinchaichote, S. K. Nguang, and P. Shi, \"H\u221e 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.\n[11]\tS. H. Kim and P. Park, \"H\u221e 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.\n[12]\tW. Assawinchaichote, \"Synthesis of a robust H\u221e 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.\n[13]\tN. 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.\n[14]\tW. 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.\n[15]\tH. Gassara, A. EI Hajjaji and M. Chaabane, \"Observer-based robust H\u221e reliable control for uncertain T-S fuzzy systems with state time delay,\" IEEE Trans. Fuzzy Syst. vol.18, no.6, 2010 pp. 1027-1040.\n[16]\tJ. Luo, Y. Liu, Y. Dong and X. Min, \"State-derivative-dependent robust H\u221e controller design for T-S fuzzy time-delay systems,\" IEEE Conference. Chinese cont. and Decision.,2010, pp. 311-316.\n[17]\t 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.\n[18]\tG. 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.\n[19]\tT. 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.\n[20]\tR. 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: http://www.cdn.intechopen.com/pdfs/5339.pdf ), 2008, pp. 1-28.\n[21]\tF. 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."]}

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

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This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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