Youla Parameterization and Design of Takagi-Sugeno Fuzzy Control Systems

  • Wei Xie
  • Toshio Eisaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4223)


A method of designing Takagi-Sugeno fuzzy control systems based on the parameterization of quadratically stabilizing controllers is presented. Conception of doubly coprime factorization and Youla parameterization of LTI systems are extended to T-S fuzzy system with respect to quadratic stability. The parameterization of the close-loop systems, which are affine with arbitrary stable Q-parameter, is then described. This description enables the application of the Q-parameter approach to various T-S fuzzy control-systems. Above all, a design scheme of Q to obtain L2-gain performance is clarified.


Fuzzy System Linear Matrix Inequality Linear Time Invariant System Fuzzy Control System Quadratic Lyapunov Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Castro, J.: Fuzzy Logic controllers are Universal Approximators. IEEE Transactions on Systems, Man and Cybernetics 25, 629–635 (1995)CrossRefGoogle Scholar
  2. 2.
    Tanaka, K., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man and Cybernetics 15(1), 116–132 (1985)Google Scholar
  3. 3.
    Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequality in Systems and Control Theory. SIAM Studies in Applied Mathematics, vol. 15. SIAM, Philadelphia (1994)Google Scholar
  4. 4.
    Wang, H.O., Tanaka, K., Griffin, M.F.: An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues. IEEE Trans. Fuzzy Sys. 4(1), 14–23 (1996)CrossRefGoogle Scholar
  5. 5.
    Johansson, M., Rantzer, A., Arzen, K.E.: Piecewise Quadratic Stability for Affine Sugeno Systems. In: Proc. 7th IEEE Int. Conf. Fuzzy Syst., Anchorage, AK, vol. 1, pp. 55–60 (1998)Google Scholar
  6. 6.
    Petterson, S., Lennartson, B.: An LMI Approach for Stability Analysis of Nonlinear Systems. In: Proc. of European Control Conference, ECC 1998, Brussels, Belgium (1997)Google Scholar
  7. 7.
    Tanaka, K., Sugeno, M.: Stability Analysis and Design of Fuzzy Control systems. Fuzzy Sets and systems 45(2), 135–156 (1992)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Tanaka, K., Ikeda, T., Wang, H.O.: Design of Fuzzy Control Systems Based on Relaxed LMI Stability Conditions. In: Proc. 35th CDC, pp. 598–603 (1996)Google Scholar
  9. 9.
    Li, J., Wang, H.O., Niemann, D., Tanaka, K.: Dynamic parallel distributed compensation for Takagi-Sugeno fuzzy systems: An LMI approach. Inf. Sci. 123(3-4), 201–221 (2000)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Youla, D.C., Jabr, H., Bongiorno, J.J.: Modern Wiener-Hopf design of optimal control controllers: part II: The multivariable case. IEEE Trans. Autom. Control 21, 319–338 (1976)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kučera, V.: Discrete linear Control: the Polynomial Equation Approach. Wiley, New York (1979)MATHGoogle Scholar
  12. 12.
    Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI control toolbox for use with matlab, User’s guide, The Math Works Inc Natick, MA, USA (1995)Google Scholar
  13. 13.
    Masubuchi, I., Ohara, A., Suda, N.: LMI based controller synthesis: A unified formulation and solution. International Journal of Robust and Nonlinear Control 8(8), 669–686 (1998)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wei Xie
    • 1
  • Toshio Eisaka
    • 2
  1. 1.College of Automation Science and TechnologySouth China University of TechnologyGuangzhouChina
  2. 2.Computer Sciences, Kitami institute of TechnologyHokkaidoJapan

Personalised recommendations