Homogeneous polynomially nonquadratic stabilization of discrete-time TakagiSugeno systems via nonparallel distributed compensation law

IEEE Transactions on Fuzzy Systems

Volumn 18, Issue 5, 2010, Pages 994-1000

  Ding, Baocang ^a  

^a CHONGQING UNIVERSITY   (China)

Author keywords

Fuzzy control; homogeneous polynomial; nonquadratic Lyapunov function; Plyas theorem; stability

Indexed keywords

COMPENSATION LAW; DISCRETE-TIME; DISCRETE-TIME NONLINEAR SYSTEMS; HOMOGENEOUS POLYNOMIALS; LYAPUNOV; NONQUADRATIC STABILIZATION; PARAMETER-DEPENDENT LINEAR MATRIX INEQUALITY; PARAMETERIZED; PLYAS THEOREM; STABILITY CONDITION; SUFFICIENT CONDITIONS; TAKAGI-SUGENO; TAKAGI-SUGENO SYSTEMS; TECHNIQUES USED;

DIFFERENTIAL EQUATIONS; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; POLYNOMIALS;

FREQUENCY SELECTIVE FADING;

EID: 77957815243     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2010.2053210     Document Type: Article

References (24)

1. P. A. Bliman, "An existence result for polynomial solutions of parameterdependent LMIs", Syst. Control Lett., vol. 51, no. 3/4, pp. 165-169, 2004.
2. P. A. Bliman, R. C. L. F. Oliveira, V. F. Montagner, and P. L. D. Peres, "Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex", in Proc. 45th IEEE-CDC, San Diego, CA, 2006, pp. 1486-1491.
3. B. Ding, "Poly-quadratic stability of discrete-time nonlinear systems in Takagi-Sugeno's form", Asian J. Control, vol. 11, no. 6, pp. 610-619, 2009.
4. B. Ding, "Stabilization of Takagi-Sugeno model via non-parallel distributed compensation law", IEEE Trans. Fuzzy Syst., vol. 18, no. 1, pp. 188-194, Feb. 2010.
5. B. Ding and B. Huang, "Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi-Sugeno's form", Int. J. Syst. Sci., vol. 39, no. 5, pp. 487-496, 2008.
6. B. Ding, H. Sun, and P. Yang, "Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form", Automatica, vol. 42, no. 3, pp. 503-508, 2006.
7. C. H. Fang, Y. S. Liu, S. W. Kau, L. Hong, and C. H. Lee, "A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems", IEEE Trans. Fuzzy Syst., vol. 14, no. 3, pp. 386-397, Jun. 2006.
8. G. Feng, "Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions", IEEE Trans. Fuzzy Syst., vol. 12, no. 1, pp. 22-28, Feb. 2004.
9. ∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities", IEEE Trans. Fuzzy Syst., vol. 13, no. 1, pp. 94-103, Feb. 2005.
10. T. M. Guerra and L. Vermeiren, "LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form", Automatica, vol. 40, no. 5, pp. 823-829, 2004.
11. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed. Cambridge, U. K.: Cambridge Univ. Press, 1952.
12. M. Johansson, A. Rantzer, and K. Arzen, "Piecewise quadratic stability of fuzzy systems", IEEE Trans. Fuzzy Syst., vol. 7, no. 6, pp. 713-722, Dec. 1999.
13. E. Kim and H. Lee, "New approaches to relaxed quadratic stability condition of fuzzy control systems", IEEE Trans. Fuzzy Syst., vol. 8, no. 5, pp. 523-533, Oct. 2000.
14. D. H. Lee, J. B. Park, and Y. H. Joo, "Improvement on nonquadratic stabilization of discrete-time Takagïc-Sugeno fuzzy systems: Multipleparameterization approach", IEEE Trans. Fuzzy Syst., vol. 18, no. 2, pp. 425-429, Apr. 2010.
15. ∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI", Automatica, vol. 39, no. 9, pp. 1571-1582, 2003.
16. V. F. Montagner, R. C. L. F Oliveira, and P. L. D. Peres, "Necessary and sufficient LMI conditions to compute quadratically stabilizing state feedback controllers for Takagi-Sugeno systems", in Proc. Amer. Control Conf., New York, NY, 2007, pp. 4059-4064.
17. R. C. L. F Oliveira and P. L. D. Peres, "Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameterdependent solutions via LMI relaxations", IEEE Trans. Autom. Control, vol. 52, no. 7, pp. 1334-1340, Jul. 2007.
18. V. Powers and B. Reznick, "A new bound for Pólya's theorem with applications to polynomials positive polyhedra", J. Pure Appl. Algebra, vol. 164, no. 1/2, pp. 221-229, 2001.
19. A. Sala and C. Arino, "Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Application of Polya's theorem", Fuzzy Sets Syst., vol. 158, no. 24, pp. 2671-2686, 2007.
20. C. Scherer, "Relaxations for robust linear matrix inequality problems with verification for exactness", SIAM J. Matrix Anal. Appl., vol. 27, no. 2, pp. 365-395, 2005.
21. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control", IEEE Trans. Syst., Man Cybern., vol. SMC-15, no. 1, pp. 116-132, Feb. 1985.
22. K. Tanaka, T. Hori, and H. O. Wang, "A multiple Lyapunov function approach to stabilization of fuzzy control systems", IEEE Trans. Fuzzy Syst., vol. 11, no. 4, pp. 582-589, Aug. 2003.
23. K. Tanaka, T. Ikeda, and H. O. Wang, "Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs", IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 250-265, May 1998.
24. H. O. Wang, K. Tanaka, and M. Griffin, "An approach to fuzzy control of nonlinear systems: Stability and design issues", IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14-23, Feb. 1996.(Pubitemid 126782417)