Have a personal or library account? Click to login
A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models Cover

A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models

International Journal of Applied Mathematics and Computer Science
Volume 17 (2007): Issue 1 (March 2007)
By: Ibtissem Abdelmalek,  Noureddine Goléa and  Mohamed Hadjili  
Open Access
|Apr 2007

References

  1. Bernal M. and Hušek P. (2005): Non-quadratic performance design for Takagi-Sugeno fuzzy systems. — Int. J. Appl. Math. Comput. Sci., Vol. 15, No. 3, pp. 383-391.
    Search in Google Scholar
  2. Blanco Y., Perruquetti W. and Borne P. (2001): Non-quadratic stability of nonlinear systems in the Takagi-Sugeno form. — Proc. European Control Conference, ECC, Porto, Portugal, pp. 3917-3922.10.23919/ECC.2001.7076546
    Search in Google Scholar
  3. Boyd S., El Ghaoui L., Feron E. and Balakrishnan B. (1994): Linear Matrix Inequalities in Systems and Control Theory. — Philadelphia: SIAM.10.1137/1.9781611970777
    Search in Google Scholar
  4. Cao Y-Y and Lin Z. (2003): Robust stability analysis and fuzzy schduling control for nonlinear systems subject to actuator saturation. — IEEE Trans. Fuzzy Syst., Vol. 11, No. 1, pp. 57-67.
    Search in Google Scholar
  5. Cao S.G., Rees N.W. and Feng G. (1997): Analysis and design of a class of complex control systems. — Automatica, Vol. 33, No. 6, pp. 1029-1039.
    Search in Google Scholar
  6. Chadli M., Maquin D., Ragot J. (2000): Relaxed stability conditions for Takagi-Sugeno fuzzy systems. — Proc. IEEE Int. Conf. Systems, Man and Cybernetics, SMC, Nashville, TN, pp. 3514-3519.10.1109/ICSMC.2000.886553
    Search in Google Scholar
  7. Chadli M., Maquin D., Ragot J. (2001): On the stability analysis of multiple model systems. — Proc. European Control Conference, ECC, Porto, Portugal, pp. 1894-1899.10.23919/ECC.2001.7076198
    Search in Google Scholar
  8. Chadli M., Maquin D., Ragot J. (2005): Stability analysis and design for continuous-time Takagi-Sugeno control systems. — Int. J. Fuzzy Syst., Vol. 7, No. 3, pp. 101-109.
    Search in Google Scholar
  9. Feng G. (2002): An approach to adaptive control of fuzzy dynamic systems. — IEEE Trans. Fuzzy Syst., Vol. 10, No. 2, pp. 268-275.10.1109/91.995127
    Search in Google Scholar
  10. Hadjili M.L. (2002): Fuzzy logic in nonlinear modeling and control. — Ph.D. thesis, CESAME, UCL, Belgium.
    Search in Google Scholar
  11. Jadbabaie A. (1999): A reduction in conservatism in stability and L2 gain analysis of Takagi-Sugeno fuzzy systems via linear matrix inequalities. — Proc. 14th IFAC Triennial World Congress, Beijing, China, pp. 285-289.
    Search in Google Scholar
  12. Johansson M. (1999): Piecewise linear control systems. — Ph.D. thesis, Lund Institute of Technology, Lund, Sweden.
    Search in Google Scholar
  13. Johansson M., Rantzer A. and Årzén K-E. (1999): Piecewise quadratic stability of fuzzy systems. — IEEE Trans. Fuzzy Syst., Vol. 4, No. 6, pp. 713-722.10.1109/91.811241
    Search in Google Scholar
  14. Khalil H.K. (1996): Nonlinear Systems, 2nd Ed., — Upper Saddle River, NJ: Prentice-Hall.
    Search in Google Scholar
  15. Korba P., Babuška R., Verbruggen H.B. and Frank P.M. (2003): fuzzy gain scheduling: controller and observer design based on Lyapunov method and convex optimization. — IEEE Trans. Fuzzy Syst., Vol. 11, No. 3, pp. 285-298.10.1109/TFUZZ.2003.812680
    Search in Google Scholar
  16. Lee H.J., Park J.B. and Chen G. (2001): Robust fuzzy control of nonlinear systems with parametric uncertainties. — IEEE Trans. Fuzzy Syst., Vol. 9, No. 2, pp. 369-379.10.1109/91.919258
    Search in Google Scholar
  17. Morère Y. (2001): Mise en oeuvre de lois de commande pour les modèles flous de type Takagi-Sugeno. — Ph.D. thesis, LAMIH, Université de Valenciennes et du Haut Cambrésis, France.
    Search in Google Scholar
  18. Ohtake H., Tanaka K. and Wang H.O. (2003): Piecewise nonlinear control. — Proc. 42nd IEEE Conf. Decision and Control, Maui, HI, (CD-ROM).
    Search in Google Scholar
  19. Takagi T. and Sugeno M. (1985): Fuzzy identification of systems and its applications to modeling and control. — IEEE Trans. Syst. Man Cybern., Vol. SMC-15, No. 1, pp. 116-132.10.1109/TSMC.1985.6313399
    Search in Google Scholar
  20. Tanaka K. and Sugeno M. (1992): Stability analysis and design of fuzzy control systems. — Fuzzy Sets Syst., Vol. 45, No. 2, pp. 135-156.10.1016/0165-0114(92)90113-I
    Search in Google Scholar
  21. Tanaka K. and Wang H.O. (2001): Fuzzy Control Systems Design and Analysis. A Linear Matrix Inequalities Approach. — New York: Wiley.
    Search in Google Scholar
  22. Tanaka K., Ikeda T. and Wang H.O. (1996): Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, H∞ control theory, and linear matrix inequalities. — IEEE Trans. Fuzzy Syst., Vol. 4, No. 1, pp. 1-13.10.1109/91.481840
    Search in Google Scholar
  23. Tanaka K., Hori T. and Wang H.O. (2001a): A dual design problem via multiple Lyapunov functions. — Proc. 10th IEEE Int. Conf. Fuzzy Systems, Melbourne, Australia.
    Search in Google Scholar
  24. Tanaka K., Hori T. and Wang H.O. (2001b): A fuzzy Lyapunov approach to fuzzy control system design. — Proc. American Control Conf., Arlington VA, Washington CD, pp. 4790-4795.10.1109/ACC.2001.945740
    Search in Google Scholar
  25. Tanaka K., Hori T. and Wang H.O. (2001c): New parallel distributed compensation using time derivative membership functions: A fuzzy Lyapunov approach. — Proc. 40th IEEE Conf. Decision and Control, Orlando, FL, pp. 3942-3947.
    Search in Google Scholar
  26. Tanaka K., Hori T. and Wang H.O. (2003): A multiple Lyapunov function approach to stabilization of fuzzy control systems. — IEEE Trans. Fuzzy Syst., Vol. 11, No. 4, pp. 582-589.10.1109/TFUZZ.2003.814861
    Search in Google Scholar
  27. Tsen C-S, Chen B-S and Uang H-J (2001): Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model. — IEEE Trans. Fuzzy Syst., Vol. 9, No. 3, pp. 381-392.
    Search in Google Scholar
  28. Wang H.O., Tanaka K. and Griffin M. (1995): Parallel distributed compensation of nonlinear systems by Takagi and Sugeno's fuzzy model. — Proc. 4th IEEE. Int. Conf. Fuzzy Systems, Yokohama, Japan, pp. 531-538.
    Search in Google Scholar
  29. Wang H.O., Tanaka K. and Griffin M.F. (1996): An approach to fuzzy control of nonlinear systems: Stability and design issues. — IEEE Trans. Fuzzy Syst., Vol. 4, No. 1, pp, 14-23.10.1109/91.481841
    Search in Google Scholar
  30. Wong L.K., Leung F.H.F. and Tam P.K.S. (1998): Lyapunov-function-based design of fuzzy logic controllers and its application on combining controllers. — IEEE Trans. Industr. Electron., Vol. 45, No. 3, pp. 502-509.10.1109/41.679009
    Search in Google Scholar
  31. Zhao J. (1995): System modeling, identification and control using fuzzy logic. — Ph.D. thesis, CESAME, UCL, Belgium.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10006-007-0005-4 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Journal RSS Feed
Language: English
Page range: 39 - 51
Published on: Apr 5, 2007
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
T-S fuzzy systems,
non-quadratic stability conditions,
linear matrix inequalities,
parallel distributed compensation,
stabilization
Related subjects:
Mathematics,
Applied mathematics

© 2007 Ibtissem Abdelmalek, Noureddine Goléa, Mohamed Hadjili, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 17 (2007): Issue 1 (March 2007)