Improvement on nonquadratic stabilization of discrete-time Takagi-Sugeno fuzzy systems: Multiple-parameterization approach

IEEE Transactions on Fuzzy Systems

Volumn 18, Issue 2, 2010, Pages 425-429

  Lee, Dong Hwan ^a   Park, Jin Bae ^a   Joo, Young Hoon ^b  

^a Yonsei University   (South Korea)

^b Kunsan National University   (South Korea)

Author keywords

Discrete time Takagi Sugeno (TS) fuzzy systems; Linear matrix inequality (LMI); Multidimensional fuzzy summations; Multipleparameterization nonparallel distributed compensation (non PDC) control law

Indexed keywords

ALGEBRAIC PROPERTIES; ASYMPTOTIC STABILIZABILITY; CONTROL LAWS; CONVEX PROGRAMMING; DISCRETE-TIME; FUZZY CONTROLLERS; HOMOGENEOUS POLYNOMIALS; NONQUADRATIC STABILIZATION; NUMERICALLY TRACTABLE; SUFFICIENT CONDITIONS; TAKAGI SUGENO FUZZY SYSTEMS; WEIGHTING FUNCTIONS;

COMMUNICATION CHANNELS (INFORMATION THEORY); DELAY CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; FUZZY CONTROL; FUZZY SYSTEMS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; STABILIZATION;

DISCRETE TIME CONTROL SYSTEMS;

EID: 77950660190     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2010.2042720     Document Type: Article

References (31)

1. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis. Ed. New York: Wiley, 2001
2. 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)
3. 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. (Pubitemid 128750059)
4. 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. 523-534, Oct. 2000.
5. X. Liu and Q. Zhang, "Approaches to quadratic stability condisitons and HΣ control designs for T-S fuzzy systems," IEEE Trans. Fuzzy Syst., vol.11, no.6, pp. 830-839, Dec. 2003.
6. 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)
7. A. Sala and C. Ariño, "Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Ṕolya's theorem," Fuzzy Sets Syst., vol.158, no.24, pp. 2671-2686, 2007. (Pubitemid 47513206)
8. A. Sala and C. Ariño, "Design of multiple-parameterisation PDC controllers via relaxed conditions for multi-dimensional fuzzy summations," in Proc. IEEE Int. Conf. Fuzzy Syst., 2007, pp. 1-6.
9. 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., vol.37, no.3, pp. 727-732, Jun. 2007. (Pubitemid 46784606)
10. 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.
11. M. Johansson, A. Rantzer, and K. E. Å rzén, "Piecewise quadratic stability of fuzzy systems," IEEE Trans. Fuzzy Syst., vol.7, no.6, pp. 713-722, Dec. 1999. (Pubitemid 32212162)
12. G. Feng, "Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions," IEEE Trans. Fuzzy Syst., vol.11, no.5, pp. 605-612, Oct. 2003.
13. 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.
14. T. M. Guerra and L. Vermeiren, "LMI-based relaxed nonquadratic stabilization condttions for nonlinear systems in the Takagi-Sugeno's form," Automatica, vol.40, no.5, pp. 823-829, 2004.
15. B. C. Ding, H. X. 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. (Pubitemid 43131462)
16. A. Kruszewski and T. M. Guerra, "New approaches for the stabilization of discrete Takagi-Sugeno fuzzy models," presented at the IEEE Conf. Decis. Control/Eur. Control Conf., Seville, Spain, 2005. (Pubitemid 46297472)
17. A. Kruszewski, R. Wang, and T. M. Guerra, "Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time T-S fuzzy models: A new approach," IEEE Trans. Autom. Control, vol.53, no.2, pp. 606-611, Mar. 2008. (Pubitemid 351493901)
18. T. M. Guerra, A. Kruszewski, andM. Bernal, "Control law proposition for the stabilization of discrete Takagi-Sugeno models," IEEE Trans. Fuzzy Syst., vol.17, no.3, pp. 724-731, Jun. 2009.
19. H. K. Lam and F. H. F. Leung, "LMI-based stability and performance conditions for continuous-time nonlinear systems in Takagi-Sugeno's form," IEEE Trans. Syst.,Man Cybern., vol.37, no.5, pp. 1396-1406, Oct. 2007.
20. 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.
21. V. F. Montagner, R. C. L. F. Oliveira, and P. L. D. Peres, "Convergent LMI relaxations for quadratic stabillizability andHσ control ofTakagi-Sugeno fuzzy systems," IEEE Trans. Fuzzy Syst., vol.17, no.4, pp. 863-873, Aug. 2009.
22. D. W. Kim, J. B. Park, and Y. H. Joo, "Multirate digital control for fuzzy systems: LMI-based design and stability anaylsis," Int. J. Control, Autom., Syst., vol.4, no.4, pp. 506-515, 2006. (Pubitemid 44186843)
23. H. J. Lee, J. B. Park, and Y. H. Joo, "Robust switching-type fuzzy-modelbased output tracker," Int. J. Control, Autom., Syst., vol.3, no.3, pp. 411- 418, 2005.
24. D. W. Kim, J. B. Park, and Y. H. Joo, "Effective digital implementation of fuzzy control systems based on approximate discrete-time models," Automatica, vol.43, no.10, pp. 1671-1683, 2007.
25. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Homogeneous Lyapunov functions for systems with structured uncertainties," Automatica, vol.39, no.6, pp. 1027-1035, 2003.
26. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Polynomially parameterdependent Lyapunov functions for robust stability of polytopic systems: An LMI approach," IEEE Trans. Autom. Control, vol.50, no.3, pp. 365- 370, Mar. 2005. (Pubitemid 40448586)
27. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Robust stability of timevarying polytopic systems via parameter-dependent homogeneous Lyapunov functions," Automatica, vol.43, no.2, pp. 309-316, 2007. (Pubitemid 46037598)
28. R. C. L. F. Oliveira and P. L. D. Peres, "LMI conditions for robust stability analysis based on polynoially parameter dependent Lyapunov functions," Syst. Control Lett., vol.55, no.1, pp. 52-61, 2006. (Pubitemid 41737282)
29. 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.
30. G. H. Hardy, J. E. Littlewood, and G. Ṕolya, Inequalities, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1952.
31. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox. Natick, MA: MathWorks, 1995.