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H∞ Takagi-Sugeno Fuzzy State-Derivative Feedback Control Design for Nonlinear Dynamic Systems
Abstract: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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1129960Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 423
 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∞ 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∞ 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∞ 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∞ 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∞ 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∞ 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∞ 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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.
 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: http://www.cdn.intechopen.com/pdfs/5339.pdf ), 2008, pp. 1-28.
 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.