LMI-based stability analysis for fuzzy-model-based control systems using artificial TS fuzzy model

IEEE Transactions on Fuzzy Systems

Volumn 19, Issue 3, 2011, Pages 505-513

  Lam, H K ^a  

^a KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Fuzzy control; linear matrix inequality (LMI); stability analysis; staircase membership functions; TakagiSugeno (TS) fuzzy model

Indexed keywords

DESIGN FLEXIBILITY; FUZZY CONTROLLERS; INFINITE NUMBERS; LYAPUNOV STABILITY THEORY; SIMULATION EXAMPLE; STABILITY ANALYSIS; STABILITY CONDITION; STAIRCASE MEMBERSHIP FUNCTIONS; SYSTEM INFORMATION; T-S FUZZY MODELS; TAKAGI-SUGENO FUZZY MODELS;

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEMS; CONTROLLERS; FUZZY CONTROL; FUZZY LOGIC; FUZZY SETS; LINEAR MATRIX INEQUALITIES; MEMBERSHIP FUNCTIONS; STABILITY; STAIRS;

CONTROL SYSTEM STABILITY;

EID: 79957999813     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2011.2116027     Document Type: Article

References (22)

1. 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)
2. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Sys., Man., Cybern., vol. SMC-15, no. 1, pp. 116-132, Jan. 1985.
3. M. Sugeno and G. T. Kang, "Structure identification of fuzzy model," Fuzzy Sets Syst., vol. 28, pp. 15-33, 1988.
4. K. Tanaka and M. Sugeno, "Stability analysis and design of fuzzy control systems," Fuzzy Sets Syst., vol. 45, pp. 135-156, 1992.
5. C. L. Chen, P. C. Chen, and C. K. Chen, "Analysis and design of fuzzy control system," Fuzzy Sets Syst., vol. 57, no. 2, 26, pp. 125-140, Jul. 1993.
6. H. K. Lam and F. H. F. Leung, "Stability analysis and synthesis 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)
7. 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.
8. A. Sala and C. Ariño, "Extensions toStability analysis of fuzzy control systems subject to uncertain grades of membership," IEEE Trans. Syst., Man Cybern, B, Cybern., vol. 38, no. 2, pp. 558-563, Apr. 2008. (Pubitemid 351479575)
9. H. O. Wang, K. Tanaka, and M. F. Griffin, "An approach to fuzzy control of nonlinear systems: stability and the design issues," IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14-23, Feb. 1996. (Pubitemid 126782417)
10. K. Tanaka, T. Ikeda, and H. O.Wang, "Fuzzy regulator and fuzzy observer: Relaxed stability conditions and LMI-based designs," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 250-265, May 1998. (Pubitemid 128750059)
11. W. J. Wang, S. F. Yan, and C. H. Chiu, "Flexible stability criteria for a linguistic fuzzy dynamic system," Fuzzy Sets Syst., vol. 105, no. 1, pp. 63-80, Jul. 1999.
12. E. Kim and H. Lee, "New approaches to relaxed quadratic stability conditions of fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 523-534, Oct. 2000.
13. X. Liu and Q. Zhang, "New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI," Automatica, vol. 39, no. 9, pp. 1571-1582, Sep. 2003.
14. X. Liu and Q. Zhang, "Approaches to quadratic stability conditions and H∞ control designs for T-S fuzzy systems," IEEE Trans. Fuzzy Syst., vol. 11, no. 6, pp. 830-839, Dec. 2003.
15. M. C. M. Teixeira, E. Assunç ̃ao, and R. G. Avellar, "On relaxed LMIbased designs for fuzzy regulators and fuzzy observers," IEEE Trans. Fuzzy Syst., vol. 11, no. 5, pp. 613-623, Oct. 2003.
16. C. H. Fang, Y. S. Liu, S. W. Kau, L. Hong, and C. H. Lee, "A new LMIbased approach to relaxed quadratic stabilization of T-S fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 14, no. 3, pp. 386-397, Jun. 2006. (Pubitemid 43898881)
17. 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. 151, no. 24, pp. 2671-2686, Dec. 2007. (Pubitemid 47513206)
18. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory (SIAM Studies in Applied Mathematics). Philadelphia, PA: SIAM, 1994.
19. A. Sala and C. Ariño, "Relaxed stability and performance conditions for Takagi-Sugeno fuzzy systems with knowledge on membership-function overlap," IEEE Trans. Syst., Man, Cybern, B, Cybern., vol. 37, no. 3, pp. 727-732, Jun. 2007. (Pubitemid 46784606)
20. M. Bernal, T. M. Guerra, and A. Kruszewski, "A membership- functiondependent approach for stability analysis and controller synthesis of Takagi-Sugeno models," Fuzzy Sets Syst., vol. 160, no. 19, pp. 2776-2795, Oct. 2009.
21. 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.
22. J. J.E. Slotine andW. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991.