Non-fragile Robust H ∞  Fuzzy Controller Design for a Class of Nonlinear Descriptor Systems with Time-Varying Delays in States

  • Junsheng Ren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4223)


The controller fragility can cause the performance debasement of the closed-loop system due to small perturbations in the coefficients of the controller design, and is one of the most important factors to be considered during practical controller design. To take the controller fragility into consideration for a class of nonlinear time-delayed descriptor systems with norm-bounded time-varying uncertainties in the matrices of state, delayed state and control gain, we have proposed non-fragile robust H  ∞  fuzzy control design via state feedback controllers in this paper. The nonlinear descriptor system is approximated by Takagi-Sugeno (T-S) fuzzy model. In combination of parallel-distributed compensation (PDC) scheme, sufficient conditions are derived for the existence of non-fragile robust H  ∞  fuzzy controllers in terms of linear matrix inequalities (LMI). Finally, an example is given to demonstrate the use of the proposed controller design.


Linear Matrix Inequality Fuzzy Model Fuzzy Controller Singular System State Feedback Controller 
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.
    Keel, L.H., Bhattacharryya, S.P.: Robust, fragile, or optimal? IEEE Trans. Automat. Contr. 42, 1098–1105 (1997)MATHCrossRefGoogle Scholar
  2. 2.
    An, S., Huang, L., Gu, S., Wang, J.: Robust non-fragile state feedback control of discrete time-delay systems. In: Proceedings of International Conference on Control and Automation, Budapest, Hungary, pp. 794–799 (2005)Google Scholar
  3. 3.
    Yang, G.H., Wang, J.L.: Non-fragile nonlinear H  ∞  control via dynamic output feedback. In: Proc. Am. Control Conf., Denver, USA, pp. 2969–2972 (2003)Google Scholar
  4. 4.
    Campbell, S.L.: Singular systems of differential equations. Pitman, Marshfield (1980)MATHGoogle Scholar
  5. 5.
    Li, X., De Souza, C.E.: Criteria for robust stability and stabilization of uncertain linear systems with state-delay. Automatica 33, 1657–1662 (1997)CrossRefGoogle Scholar
  6. 6.
    Chen, S.J., Lin, J.L.: Robust stability of discrete time-delay uncertain singular systems. IEE Proc. Control Theory Appl. 150, 325–330 (2003)CrossRefGoogle Scholar
  7. 7.
    Ma, S.: Robust stabilization for a class of uncertain discrete-time singular systems with time-delays. In: Proc. World Congr. Intelligent Control Autom., Hangzhou, P.R. China, pp. 970–974 (2004)Google Scholar
  8. 8.
    Ying, H.: Sufficient conditions on uniform approximation of multivariate functions by general Tagaki-Sugeno fuzzy systems with linear rule consequence. IEEE Trans. Syst. Man, Cybern. 28, 515–521 (1998)CrossRefGoogle Scholar
  9. 9.
    Wang, H.O., Li, J., Tanaka, K.: T-S fuzzy model with linear rule consequence and PDC controller: A universal framework for nonlinear control systems. International Journal of Fuzzy Systems 5, 106–113 (2003)MathSciNetGoogle Scholar
  10. 10.
    Wang, H.O., Tanaka, K., Griffin, M.F.: Parallel distributed compensation of nonlinear systems by Takagi-Sugeno fuzzy model. In: Proc. IEEE Int. Conf. Fuzzy Syst., Yokohama, pp. 531–538 (1995)Google Scholar
  11. 11.
    Taniguchi, T., Tanaka, K., Yamafuji, K., Wang, H.O.: Fuzzy descriptor systems: Stability analysis and design via LMIs. In: Proc. Am. Control Conf., San Deigo, pp. 1827–1831 (1999)Google Scholar
  12. 12.
    Liu, G.Y., Zhang, Q.L., Yang, L., Zhai, D.: Quadratic stability study for a class of T-S fuzzy descriptor systems. Journal of Northeastern University 25, 1131–1133 (2004)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Junsheng Ren
    • 1
  1. 1.Key Laboratory of Marine Simulation & ControlDalian Maritime UniversityP.R. China

Personalised recommendations