Polynomial fuzzy-model-based control systems: Stability analysis via piecewise-linear membership functions

IEEE Transactions on Fuzzy Systems

Volumn 19, Issue 3, 2011, Pages 588-593

  Lam, H K ^a  

^a KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Fuzzy model based (FMB) control; piecewise linear membership functions (PLMFs); polynomial fuzzy systems; stability analysis; sum of squares (SOS)

Indexed keywords

DESIGN FLEXIBILITY; FINITE NUMBER; FUZZY CONTROLLERS; FUZZY MODELS; FUZZY-MODEL-BASED (FMB) CONTROL; MATHEMATICAL TOOLS; PIECEWISE-LINEAR; SAMPLE POINT; SIMULATION EXAMPLE; STABILITY ANALYSIS; STABILITY CONDITION; SUM OF SQUARES;

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEMS; CONTROLLERS; FUZZY SETS; MATHEMATICAL MODELS; MEMBERSHIP FUNCTIONS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS; SYSTEMS ENGINEERING;

CONTROL SYSTEM STABILITY;

EID: 79957983120     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2011.2118215     Document Type: Review

References (17)

1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modelling and control," IEEE Trans. Sys., Man., Cybern., vol. SMC-15, no. 1, pp. 116-132, Jan. 1985.
2. M. Sugeno and G. T. Kang, "Structure identification of fuzzy model," Fuzzy Sets Syst., vol. 28, no. 1, pp. 15-33, Oct. 1988.
3. G. Feng, "A survey on analysis and design of model-based fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 14, no. 5, pp. 676-697, Oct. 2006. (Pubitemid 44607782)
4. A. Sala, "On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems," Ann. Rev. Control, vol. 33, no. 1, pp. 48-58, Apr. 2009.
5. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley-Interscience, 2001.
6. S. P. Boyd, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: Soc. Ind. Appl. Math., 1994.
7. A. Sala and C. Ariño, "Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem," Fuzzy Sets Syst., vol. 158, no. 24, pp. 2671-2686, Jul. 2007. (Pubitemid 47513206)
8. H. K. Lam and F. H. F. Leung, "Stability analysis of fuzzy control systems subject to uncertain grades of membership," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 35, no. 6, pp. 1322-1325, Dec. 2005. (Pubitemid 41800431)
9. A. Sala and C. Ariño, "Relaxed stability and performance LMI conditions for Takagi-Sugeno fuzzy systems with polynomial constraints on membership function shapes," IEEE Trans. Fuzzy Syst., vol. 16, no. 5, pp. 1328-1336, Oct. 2008.
10. H. K. Lam and M. Narimani, "Stability analysis and performance deign for fuzzy-model-based control system under imperfect premisematching," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 949-961, Aug. 2009.
11. H. K. Lam and M. Narimani, "Quadratic stability analysis of fuzzy-modelbased control systems using staircase membership functions," IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 125-137, Feb. 2010.
12. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, "A sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 911-922, Aug. 2009.
13. K. Tanaka, H. Ohtake, and H. O. Wang, "Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 39, no. 2, pp. 561-567, Apr. 2009.
14. A. Sala and C. Ariño, "Polynomial fuzzy models for nonlinear control: A Taylor-series approach," IEEE Trans. Fuzzy Syst., vol. 17, no. 6, pp. 284-295, Dec. 2009.
15. S. Prajna, A. Papachristodoulou, and P. A. Parrilo, "Nonlinear control synthesis by sum-of-squares optimization: A Lyapunov-based approach," in Proc. Asian Control Conf., vol. 1, Melbourne, Vic., Australia, Feb. 2004, pp. 157-165. (Pubitemid 40455802)
16. S. Prajna, A. Papachristodoulou, and P. A. Parrilo, "Introducing SOSTOOLS: A general purpose sum of squares programming solver," in Proc. 41st IEEE Conf. Decis. Control, vol. 1, Las Vegas, NV, Dec. 2002, pp. 741-746.
17. A. Papachristodoulou and S. Prajna, "A tutorial on sum of squares techniques for system analysis," in Proc. Amer. Control Conf., Portland, OR, 2005, pp. 2686-2700. (Pubitemid 41189020)