Exponential Stability Analysis of Neural Networks with Multiple Time Delays

  • Huaguang Zhang
  • Zhanshan Wang
  • Derong Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3496)


Without assuming the boundedness, strict monotonicity and differentiability of the activation function, a result is established for the global exponential stability of a class of neural networks with multiple time delays. A new sufficient condition guaranteeing the uniqueness and global exponential stability of the equilibrium point is established. The new stability criterion imposes constraints, expressed by a linear matrix inequality, on the self-feedback connection matrix and interconnection matrices independent of the time delays. The stability criterion is compared with some existing results, and it is found to be less conservative than existing ones.


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  1. 1.
    Liao, X., 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
  2. 2.
    Arik, S.: Stability Analysis of Delayed Neural Networks. IEEE Trans. Circuits and Systems-I 47, 1089–1092 (2000)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cao, J.: Global Stability Conditions for Delayed CNNs. IEEE Trans. Circuits and Systems-I 48, 1330–1333 (2001)MATHCrossRefGoogle Scholar
  4. 4.
    Liao, X., Chen, G., Sanchez, E.N.: LMI-Based Approach for Asymptotic Stability Analysis of Delayed Neural Networks. IEEE Trans. Circuits and Systems-I 49, 1033–1039 (2002)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Van Den Driessche, P., Zou, X.: Global Attractivity in Delayed Hopfield Neural Network Models. SIAM Journal of Applied Mathematics 58, 1878–1890 (1998)MATHCrossRefGoogle Scholar
  6. 6.
    Liao, X., Wong, K.W., Wu, Z., Chen, G.: Novel Robust Stability Criteria for Interval-Delayed Hopfield Neural Networks. IEEE Trans. Circuits and Systems- I 48, 1355–1358 (2001)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Michel, A.N., Liu, D.: Qualitative Analysis and Synthesis of Recurrent Neural Networks. Marcel Dekker, New York (2002)MATHGoogle Scholar
  8. 8.
    Lu, W., Rong, L., Chen, T.: Global Convergence of Delayed Neural Network Systems. International Journal of Neural Systems 13, 193–204 (2003)CrossRefGoogle Scholar
  9. 9.
    Zhang, Q., Wei, X., Xu, J.: Global Exponential Stability of Hopfield Neural Networks with Continuously Distributed Delays. Physics Letters A 315, 431–436 (2003)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Cohen, M.A., Grossberg, S.: Absolute Stability and Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks. IEEE Trans. Systems, Man, and Cybernetics SMC-13, 815–826 (1983)MathSciNetGoogle Scholar
  11. 11.
    Michel, A.N., Farrell, J.A., Porod, W.: Qualitative Analysis of Neural Networks. IEEE Trans. Circuits Systems 36, 229–243 (1989)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Marcus, C.M., Westervelt, R.M.: Stability of Analog Neural Networks with Delay. Physics Review A 39, 347–359 (1989)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Gopalsamy, K., He, X.: Delay-Independent Stability in Bidirectional Associative Memory Networks. IEEE Trans. Neural Networks 5, 998–1002 (1994)CrossRefGoogle Scholar
  14. 14.
    Chen, T.: Global Exponential Stability of Delayed Hopfield Neural Networks. Neural Networks 14, 977–980 (2001)CrossRefGoogle Scholar
  15. 15.
    Lu, H.: On Stability of Nonlinear Continuous-Time Neural Networks with Delays. Neural Networks 13, 1135–1143 (2000)CrossRefGoogle Scholar
  16. 16.
    Zhang, J., Jin, X.: Global Stability Analysis in Delayed Hopfield Neural Network Models. Neural Networks 13, 745–753 (2000)CrossRefGoogle Scholar
  17. 17.
    Liao, X., Yu, J.: Robust Stability for Interval Hopfield Neural Networks with Time Delay. IEEE Trans. Neural Networks 9, 1042–1046 (1998)CrossRefGoogle Scholar
  18. 18.
    Cao, J., Wang, J.: Global Asymptotic Stability of a General Class of Recurrent Neural Networks with Time-Varying Delays. IEEE Trans. Circuits and Systems-I 50, 34–44 (2003)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Morita, M.: Associative Memory with Nonmonotone Dynamics. Neural Networks 6, 115–126 (1993)CrossRefGoogle Scholar
  20. 20.
    Zhang, Y., Heng, P.A., Fu, A.W.C.: Estimate of Exponential Convergence Rate and Exponential Stability for Neural Networks. IEEE Trans. Neural Networks 10, 1487–1493 (1999)CrossRefGoogle Scholar
  21. 21.
    Arik, S.: An Improved Global Stability Result for Delayed Cellular Neural Networks. IEEE Trans. Circuits and Systems-I 49, 1211–1214 (2002)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM Press, Philadelphia (1994)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Huaguang Zhang
    • 1
  • Zhanshan Wang
    • 1
    • 2
  • Derong Liu
    • 3
  1. 1.Northeastern UniversityShenyangChina
  2. 2.Shenyang Ligong UniversityShenyangP.R. China
  3. 3.University of IllinoisChicagoUSA

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