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Exponential Stability Analysis of Neural Networks with Multiple Time Delays

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Advances in Neural Networks – ISNN 2005 (ISNN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3496))

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Abstract

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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References

  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)

    Article  Google Scholar 

  2. Arik, S.: Stability Analysis of Delayed Neural Networks. IEEE Trans. Circuits and Systems-I 47, 1089–1092 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cao, J.: Global Stability Conditions for Delayed CNNs. IEEE Trans. Circuits and Systems-I 48, 1330–1333 (2001)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  5. Van Den Driessche, P., Zou, X.: Global Attractivity in Delayed Hopfield Neural Network Models. SIAM Journal of Applied Mathematics 58, 1878–1890 (1998)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  7. Michel, A.N., Liu, D.: Qualitative Analysis and Synthesis of Recurrent Neural Networks. Marcel Dekker, New York (2002)

    MATH  Google Scholar 

  8. Lu, W., Rong, L., Chen, T.: Global Convergence of Delayed Neural Network Systems. International Journal of Neural Systems 13, 193–204 (2003)

    Article  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MathSciNet  Google Scholar 

  11. Michel, A.N., Farrell, J.A., Porod, W.: Qualitative Analysis of Neural Networks. IEEE Trans. Circuits Systems 36, 229–243 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  12. Marcus, C.M., Westervelt, R.M.: Stability of Analog Neural Networks with Delay. Physics Review A 39, 347–359 (1989)

    Article  MathSciNet  Google Scholar 

  13. Gopalsamy, K., He, X.: Delay-Independent Stability in Bidirectional Associative Memory Networks. IEEE Trans. Neural Networks 5, 998–1002 (1994)

    Article  Google Scholar 

  14. Chen, T.: Global Exponential Stability of Delayed Hopfield Neural Networks. Neural Networks 14, 977–980 (2001)

    Article  Google Scholar 

  15. Lu, H.: On Stability of Nonlinear Continuous-Time Neural Networks with Delays. Neural Networks 13, 1135–1143 (2000)

    Article  Google Scholar 

  16. Zhang, J., Jin, X.: Global Stability Analysis in Delayed Hopfield Neural Network Models. Neural Networks 13, 745–753 (2000)

    Article  Google Scholar 

  17. Liao, X., Yu, J.: Robust Stability for Interval Hopfield Neural Networks with Time Delay. IEEE Trans. Neural Networks 9, 1042–1046 (1998)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  19. Morita, M.: Associative Memory with Nonmonotone Dynamics. Neural Networks 6, 115–126 (1993)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  21. Arik, S.: An Improved Global Stability Result for Delayed Cellular Neural Networks. IEEE Trans. Circuits and Systems-I 49, 1211–1214 (2002)

    Article  MathSciNet  Google Scholar 

  22. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM Press, Philadelphia (1994)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Northeastern University, Shenyang, Liaoning, 110004, China

    Huaguang Zhang & Zhanshan Wang

  2. Shenyang Ligong University, Shenyang, Liaoning, 110045, P.R. China

    Zhanshan Wang

  3. University of Illinois, Chicago, IL, 60607-7053, USA

    Derong Liu

Authors
  1. Huaguang Zhang
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  2. Zhanshan Wang
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  3. Derong Liu
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Editor information

Editors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  2. The Key Laboratory of Optoelectric Technology & Systems, Ministry of Education, China

    Xiaofeng Liao

  3. Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, 610054, Chengdu, P.R. China

    Zhang Yi

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© 2005 Springer-Verlag Berlin Heidelberg

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Zhang, H., Wang, Z., Liu, D. (2005). Exponential Stability Analysis of Neural Networks with Multiple Time Delays. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_21

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  • DOI: https://doi.org/10.1007/11427391_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25912-1

  • Online ISBN: 978-3-540-32065-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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