Robust H ∞  Control with Pole Placement Constraints for T-S Fuzzy Systems

  • Liang He
  • Guang-Ren Duan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3930)


This paper addresses the problem of designing a robust fuzzy controller for a class of uncertain fuzzy system with H  ∞  optimization and D -stability constraints on the closed-loop pole locations. Takagi and Sugeno (T-S) fuzzy models are used for the uncertain nonlinear systems. By utilizing the concept of the so-called parallel distributed compensation (PDC) method, solutions to the problem are derived in terms of a family of linear matrix inequalities and are numerically tractable via LMI techniques.


Fuzzy System Linear Matrix Inequality Fuzzy Controller Pole Placement Uncertain Nonlinear System 
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  1. 1.
    Lee, K.R., Jeung, E.T., Park, H.B.: Robust control for uncertain nonlinear via feedback: an LMI approach. Fuzzy Sets Syst. 120, 123–134 (2001)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Sing, K.N., Wudhichai, A.: H ∞  Filtering for Fuzzy Dynamical Systems With Stability Constraints. IEEE Trans. on Circ. and Syst. 50(11), 1503–1508 (2003)CrossRefGoogle Scholar
  3. 3.
    Ma, G.F., Shi, Z., Zhu, L.K., Liu, Y.Q.: Robust analysis of fuzzy guaranteed cost control for a class of time-delay systems with uncertain parameters. In: Proc. of the Int. Conf. on Machine Learning and Cybernetics, pp. 471–474 (2004)Google Scholar
  4. 4.
    Lo, J.C., Lin, Y.T.: State feedback via circle criterion for fuzzy systems subject to input saturations. In: Proc. of Int. Conf. on Networking Sensing & Control, pp. 920–925 (2004)Google Scholar
  5. 5.
    Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadephia (1994)MATHGoogle Scholar
  6. 6.
    Hong, S.K., Nam, Y.: Stable fuzzy control system design with pole-placement constraint: an LMI approach. Computers in Industry 51, 1–11 (2003)CrossRefGoogle Scholar
  7. 7.
    Fei, L.: Fuzzy pole placement design H ∞  with disturbance attenuation for uncertain nonlinear systems. In: Proc. of IEEE Conf. on Contr. Appl., vol. 1, pp. 23–25 (2003)Google Scholar
  8. 8.
    Sugeno, S., Kang, T.: Fuzzy Modeling and Control of Multilayer Incinerator. Fuzzy Sets Syst. 18, 329–346 (1986)MATHCrossRefGoogle Scholar
  9. 9.
    Xie, L.: Output feedback H ∞  control of systems with parameter uncertainty. Int. J. Control 63(4), 741–750 (1996)MATHCrossRefGoogle Scholar
  10. 10.
    Zhou, S.S., Lam, J., Xu, S.Y.: Robust control for discrete-time polytopic uncertain systems with linear fractional vertices. Journal of Control Theory and Applications 2(1), 75–81 (2004)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Graham, A.: Kronecker product and Matrix Calculus with Applications. Ellis Horwood, Chichseter (1981)Google Scholar
  12. 12.
    Yu, L.: Robust control, a Linear Matrix Inequality approach. Tsinghua University Press (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Liang He
    • 1
  • Guang-Ren Duan
    • 1
  1. 1.Center for Control Theory and Guidance TechnologyHarbin Institute of TechnologyHarbinP.R. China

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