Global Robust Stability of General Recurrent Neural Networks with Time-Varying Delays

  • Jun Xu
  • Daoying Pi
  • Yong-Yan Cao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)


This paper is devoted to global robust stability analysis of the general recurrent neural networks with time-varying parametric uncertainty and time-varying delays. To remove the dependence on the size of time-delays, Lyapunov-Razumikhin stability theorem and LMI approach are applied to derive the global robust stability conditions for the neural networks. Then delay-dependent global robust stability criteria are developed based on integrating Lyapunov-Krasovskii functional method and LMI approach. These stability criteria are in term of the solvability of linear matrix inequalities.


Linear Matrix Inequality Robust Stability Cellular Neural Network Delayed Neural Network Global Robust Stability 
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  1. 1.
    Cao, Y.Y., Sun, Y.X., Cheng, C.: Delay-Dependent Robust Stabilization of Uncertain Systems with Multiple State Delays. IEEE Trans. Automatic Control 43, 1608–1612 (1998)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Hale, J.K., Lunel, S.M.V.: Introduction to Functional Differential Equations. Applied Math. Scinces, vol. 99. Springer, New York (1993)MATHGoogle Scholar
  3. 3.
    Niculescu, S.I.: Delay Effects on Stability: An Robust Control Approach. Lecuture Notes in Control and Information Sciences. Springer, London (2001)Google Scholar
  4. 4.
    Liao, X.F., Chen, G., Sanchez, E.N.: Delay-dependent Exponential Stability Analysis of Delayed Neural Networks: An LMI Approach. Neural Networks 15, 855–866 (2002)CrossRefGoogle Scholar
  5. 5.
    Cao, J., Wang, J.: Global Asymptotic and Robust Stability of Recurrent Neural Networks with Time Delays. IEEE Trans. on Circuits and systems-I 52, 417–425 (2005)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Cao, J., Ho, D.W.C.: A General Framework for Global Asymptotic Stability Analysis of Delayed Neural Networks Based on LMI Approach. Chaos, Solitons and Fractals 24, 1317–1329 (2005)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Huang, H., Ho, D.W.C., Cao, J.: Analysis of Global Exponenital Stability and Periodic Solutions of Neural Networks with Time-varying Delays. Neual Networks 18, 161–170 (2005)CrossRefGoogle Scholar
  8. 8.
    Singh, V.: Robust Stability of Celluar Neural Networks with Delay: linear matrix inequality approach. IEE Proc.-Control Theory Appl. 151, 125–129 (2004)CrossRefGoogle Scholar
  9. 9.
    Zhang, H., Li, C., Liao, X.F.: A Note on the Robust Stability of Neural Networks with Time Delay. Chaos Solitons and Fractals 25, 357–360 (2005)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Li, C., Liao, X.F., Zhang, R., Prasad, A.: Global Robust Exponential Stability Analysis for Interval Neural Networks with Time-varying Delays. Chao, Solitons and Fractals 25, 751–757 (2005)MATHCrossRefGoogle Scholar
  11. 11.
    Chen, A., Cao, J., Huang, L.: Global Robust Stability of Interval Cellular Neural Networks with Time-varying Delays. Chaos, Solitons and Fractals 23, 787–799 (2005)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jun Xu
    • 1
    • 2
  • Daoying Pi
    • 1
  • Yong-Yan Cao
    • 1
  1. 1.National Laboratory of Industrial Control TechnologyZhejiang UniversityHangzhouP.R. China
  2. 2.College of Information & ManagementJiangxi University of Finance & EconomicsNanchangP.R. China

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