Absolutely Stable of Takagi-Sugeno Fuzzy Control System by Using Popov’s Criterion

Azhdar Soleymanpour Bakefayat, Aghileh Heydari

Department of Mathematics, Payame Noor University, Tehran, IRAN.

DOI: 10.4236/am.2012.310165                

Abstract

In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition.

Keywords

Fuzzy Control; Fuzzy Systems; Popov’s Criterion

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. Takagi and Sugeno, “Fuzzy Identification of Systems and Its Applications to Modeling and Control,” IEEE Transactions on Systems, Man, and Cybernet, Vol. 15, 1985, pp. 116-132. doi:10.1109/TSMC.1985.6313399
[2]	H. O. Wang, J. Li, D. Niemann and Tanaka, “T-S Fuzzy Model with Linear Rule Consequence and PDC Controller: A Universal Framework for Nonlinear Control Systems,” Proceedings of FUZZ-IEEE 2000, San Antonio, 7-10 May 2000, pp. 549-554.
[3]	N. Li, S. Y. Li and Y. G. Xi, “Multi-Model Predictive Control Based on the Takagi-Sugeno Fuzzy Models: A Case Study,” Information Sciences, Vol. 165, No. 3-4, 2004, pp. 247-263. doi:10.1016/j.ins.2003.10.011
[4]	C. W. Park, “LMI-Based Robust Stability Analysis for Fuzzy Feedback Linearization Regulator with Its Applications,” Information Sciences, Vol. 152, 2003, pp. 287-301. doi:10.1016/S0020-0255(03)00057-4
[5]	A. Kandel, Y. Luo and Y. Q. Zhang, “Stability Analysis of Fuzzy Control Systems,” Fuzzy Sets and Systems, Vol. 105, No. 1, 1999, pp. 33-48. doi:10.1016/S0165-0114(97)00234-0
[6]	J. J. E. Slotine and W. Li, “Applied Nonlinear Control,” Prentice-Hall, New York, 1991.
[7]	H. K. Khalil, “Nonlinear Systems Design and Control,” Vol. 2, 1950