Robust Absolute Stability Analysis for Uncertain Fuzzy Neutral Systems

  • Xiuyong Ding
  • Lan Shu
  • Changcheng Xiang
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 78)


This paper considers the robust absolute stability issues for a class of T-S fuzzy uncertain neutral systems with delays. The uncertainties considered in this paper are norm bounded, and possible time-varying. Based on Lyapunov-Krasovskii functional and linear matrix inequalities approach, the absolute robust stabilization of the fuzzy uncertain neutral systems can be achieved. Two examples are given to demonstrate the effectiveness of the proposed method.


Takagi-Sugeno (T-S) fuzzy systems neutral system absolute stability 


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  1. 1.
    Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. SMC 15, 116–132 (1985)zbMATHGoogle Scholar
  2. 2.
    Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)zbMATHGoogle Scholar
  3. 3.
    Cao, Y.Y., Frank, P.M.: Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst. 8, 200–211 (2000)CrossRefGoogle Scholar
  4. 4.
    Kolmanovskii, V., Myshkis, A.: Applied Theory of Functional Differential Equations. Kluwer Academic Publishers, Netherlands (1992)Google Scholar
  5. 5.
    Rubanik, V.P.: Oscillations of quasilinear systems having delay, Izd. Nauka, Moscow (1969)Google Scholar
  6. 6.
    Harband, J.: The existence of monotonic solutions of a nonlinear car-following equation. J. Math. Anal. Appl. 57, 257–272 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kolmanovskii, V., Myshkis, A.: Introduction to the Theory and Applications of Functional Differential Equations. Kluwer Academic Publishers, Netherlands (1999)zbMATHGoogle Scholar
  8. 8.
    Chukwu, E.N.: Mathematical controllability theory of capital growth of nations. Appl. Math. Comput. 52, 317–344 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Barone, S.R.: A new approach to some nonlinear fluid dynamics problems. Phys. Lett. A 70, 260–262 (1979)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Chen, W.H., Zheng, W.X.: Delay-dependent robust stabilization for uncertain neutral systems with distributed delays. Automatica 43, 95–104 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    He, Y., Wu, M., She, J.H., Liu, G.P.: Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays. Syst. Contr. Lett. 51, 57–65 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Sun, X., Zhao, J., Wang, W.: Two design schemes for robust adaptive control of a class of linear uncertain neutral delay systems. Int. J. Innov. Comput. Inform. Contr. 3, 385–396 (2007)Google Scholar
  13. 13.
    Yoneyama, J.: Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays. Inform. Sci. 178, 1935–1947 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Xu, S., Lam, J., Chen, B.: Robust H1 control for uncertain fuzzy neutral delay systems. Eur. J. Contr. 10, 365–380 (2004)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Li, Y., Xu, S.: Robust stabilization and H1 control for uncertain fuzzy neutral systems with mixed time delays. Fuzzy Sets Syst. 159, 2730–2748 (2008)zbMATHCrossRefGoogle Scholar
  16. 16.
    Yang, J., Zhong, S.M., Xiong, L.L.: A descriptor system approach to non-fragile H1 control for uncertain fuzzy neutral systems. Fuzzy Sets Syst. 160, 423–438 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Yoneyama, J.: Generalized conditions for H1 disturbance attenuation of fuzzy time-delay systems. IEEE Int. Conf. Syst. Man Cybern. 2, 1736–1741 (2005)CrossRefGoogle Scholar
  18. 18.
    Xie, L.: Output feedback H∞ control of systems with parameter uncertainty. Int. J. Contr. 63, 741–750 (1996)zbMATHCrossRefGoogle Scholar
  19. 19.
    Cao, Y.Y., Lin, Z.L., Shamash, Y.: Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation. Syst. Cont. Lett. 46, 137–151 (2002)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Xiuyong Ding
    • 1
  • Lan Shu
    • 1
  • Changcheng Xiang
    • 1
    • 2
  1. 1.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduP.R. China
  2. 2.Computer Science DepartmentAba Teachers CollegePixianP.R. China

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