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Global Stability of Neural Networks with Time-Varying Delays

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Adaptive and Natural Computing Algorithms (ICANNGA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4432))

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Abstract

This paper deals with the problem of global stability for a class of neural networks with time-varying delays. A new sufficient condition for global stability is proposed by using some slack matrix variables to express the relationship between the system matrices. The restriction on the derivative of the delay function to be less than unit is removed. A numerical example shows that the result obtained in this paper improves the upper bound of the delay over some existing ones.

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References

  1. Arik, S.: An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Networks 13, 1239–1242 (2002)

    Article  Google Scholar 

  2. Arik, S.: Global robust stability of delayed neural networks. IEEE Trans. Circuits Syst. I. 50, 156–160 (2003)

    Article  MathSciNet  Google Scholar 

  3. Cao, J.: A set of stability criteria for delayed cellular neural networks. IEEE Trans. Circuits Syst. I. 48, 494–498 (2001)

    Article  MATH  Google Scholar 

  4. Cao, J., Huang, D.S., Qu, Y.Z.: Global robust stability of delayed recurrent neural networks. Chaos, Solitons and Fractals 23, 221–229 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, A., Cao, J., Huang, L.: An estimation of upperbound of delays for global asymptotic stability of delayed Hopfield neural networks. IEEE Tran. Circuit Syst. I. 49, 1028–1032 (2002)

    Article  MathSciNet  Google Scholar 

  6. Chu, T.G.: Necessary and sufficient condition for absolute stability of normal neural networks. Neural Networks 16, 1223–1227 (2003)

    Article  Google Scholar 

  7. Chu, T.G.: A decomposition approach to analysis of competitive-cooperative neural networks with delay. Physics Letters A 312, 339–347 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chu, T.G.: An exponential convergence estimate for analog neural networks with delay. Physics Letters A 283, 113–118 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. He, Y., Wang, Q.G., Wu, M.: LMI-based stability criteria for neural networks with multiple time-varying delays. Physica D 212, 126–136 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Li, C.D., Liao, X.F., Zhang, R.: Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach. Physics Letters A 328, 452–462 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Liang, J.L., Cao, J.: A based-on LMI stability criterion for new criterion for delayed recurrent neural networks. Chaos, Solitons and Fractals 28, 154–160 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Liao, X.F., Wong, K.W., Wu, Z.F., Chen, G.: Novel robust stability criterion for interval-delayed Hopfield neural networks. IEEE Trans. Circuits Syst. I. 48, 1355–1359 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. Singh, V.: Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEE Proc.-Control Theory Appl. 151, 125–129 (2004)

    Article  Google Scholar 

  15. Singh, V.: Global robust stability of delayed neural networks: an LMI approach. IEEE Trans. Circuits Syst. II. 52, 33–36 (2005)

    Article  Google Scholar 

  16. Xu, S., Lam, J., Ho, D.W.C., Zou, Y.: Novel global asymptotic stability criteria for delayed cellular neural networks. IEEE Tran. Circuit Syst. II. 52, 349–353 (2005)

    Article  Google Scholar 

  17. Ye, H., Michel, A.N., Wang, K.: Global stability and local stability of Hopfield neural networks with delays. Physical Review E 59, 4206–4213 (1994)

    Article  MathSciNet  Google Scholar 

  18. Zuo, Z., Wang, Y.: Novel delay-dependent exponential stability analysis for a class of delayed neural networks. In: Huang, D.-S., Li, K., Irwin, G.W. (eds.) ICIC 2006. LNCS, vol. 4113, pp. 216–226. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  19. Zhang, H., Li, C.G., Liao, X.F.: A note on the robust stability of neural networks with time delay. Chaos, Solitons and Fractals 25, 357–360 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhang, Q., Wei, X., Xu, J.: Global asymptotic stability of Hopfield neural networks with transmission delays. Physics Letters A 318, 399–405 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Yang, H.F., Chu, T., Zhang, C.: Exponential stability of neural networks with variable delays via LMI approach. Chaos, Solitons and Fractals 30, 133–139 (2006)

    Article  MathSciNet  Google Scholar 

  22. Zuo, Z.Q., Wang, Y.J.: Global asymptotic stability analysis for neural networks with time-varying delays. In: 45th IEEE Conference on Decision and Control, San Diego, USA (2006)

    Google Scholar 

  23. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in systems and control theory. SIAM, Philadelphia (1994)

    Google Scholar 

  24. Zuo, Z.Q., Wang, Y.J.: Relaxed LMI condition for output feedback guaranteed cost control of uncertain discrete-time systems. Journal of Optimization Theory and Applications 127, 207–217 (2005)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Electrical Engineering & Automation, Tianjin University, Tianjin, 300072, China

    Yijing Wang & Zhiqiang Zuo

Authors
  1. Yijing Wang
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  2. Zhiqiang Zuo
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Editor information

Bartlomiej Beliczynski Andrzej Dzielinski Marcin Iwanowski Bernardete Ribeiro

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© 2007 Springer Berlin Heidelberg

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Wang, Y., Zuo, Z. (2007). Global Stability of Neural Networks with Time-Varying Delays. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2007. Lecture Notes in Computer Science, vol 4432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71629-7_79

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  • DOI: https://doi.org/10.1007/978-3-540-71629-7_79

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71590-0

  • Online ISBN: 978-3-540-71629-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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