Skip to main content
SpringerLink
Log in

Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, the global robust exponential stability of interval neural networks with delays and inverse Hölder neuron activation functions is considered. By using linear matrix inequality (LMI) techniques and Brouwer degree properties, the existence and uniqueness of the equilibrium point are proved. By applying Lyapunov functional approach, a sufficient condition which ensures that the network is globally robustly exponentially stable is established. A numerical example is provided to demonstrate the validity of the theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Singh, V.: A new criterion for global robust stability of interval delayed neural networks. J. Comput. Appl. Math. 221, 219–225 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Singh, V.: Improved global robust stability of interval delayed neural networks via split interval: generalizations. Appl. Math. Comput. 206, 290–297 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Singh, V.: Improved global robust stability for interval-delayed Hopfield neural networks. Neural Process. Lett. 27, 257–265 (2008)

    Article  Google Scholar 

  4. Singh, V.: New LMI-based criteria for global robust stability of delayed neural networks. Appl. Math. Model. (2010). doi:10.1016/j.apm.2010.01.005

    Google Scholar 

  5. Gau, R., Lien, C., Hsieh, J.: Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach. Chaos Solitons Fractals 32, 1258–1267 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Li, T., Guo, L., Sun, C.: Robust stability for neural networks with time-varying delays and linear fractional uncertainties. Neurocomputing 71, 421–427 (2007)

    Article  Google Scholar 

  7. Ou, O.: Global robust exponential stability of delayed neural networks: an LMI approach. Chaos Solitons Fractals 32, 1742–1748 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Qi, H.: New sufficient conditions for global robust stability of delayed neural networks. IEEE Trans. Circuits Syst. I 54, 1131–1141 (2007)

    Article  Google Scholar 

  9. Qiu, J., Yang, H., Zhang, J., Gao, Z.: New robust stability criteria for uncertain neural networks with interval time-varying delays. Chaos Solitons Fractals 39, 579–585 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Qiu, J., Zhang, J., Wang, J., Xia, Y., Shi, P.: A new global robust stability criteria for uncertain neural networks with fast time-varying delays. Chaos Solitons Fractals 37, 360–368 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Shen, T., Zhang, Y.: Improved global robust stability criteria for delayed neural networks. IEEE Trans. Circuits Syst. II 54, 715–759 (2007)

    Article  MathSciNet  Google Scholar 

  12. Wang, Z., Zhang, H., Yu, W.: Robust exponential stability analysis of neural networks with multiple time delays. Neurocomputing 70, 2534–2543 (2007)

    Article  Google Scholar 

  13. Wang, Z., Zhang, H., Yu, W.: Robust stability of Cohen-Grossberg neural networks via state transmission matrix. IEEE Trans. Neural Netw. 20, 169–174 (2009)

    Article  Google Scholar 

  14. Wang, Z., Zhang, H., Yu, W.: Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay. Neurocomputing 72, 1105–1110 (2009)

    Article  Google Scholar 

  15. Wu, W., Cui, B.: Global robust exponential stability of delayed neural networks. Chaos Solitons Fractals 35, 747–754 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yu, W., Yao, L.: Global robust stability of neural networks with time varying delays. J. Comput. Appl. Math. 206, 679–687 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhang, B., Xu, S., Li, Y.: Delay-dependent robust exponential stability for uncertain recurrent neural networks with time-varying delays. Int. J. Neural Syst. 17, 207–218 (2007)

    Article  MATH  Google Scholar 

  18. Zhang, H., Wang, Z., Liu, D.: Robust stability analysis for interval Cohen-Grossberg neural networks with unknown time-varying delays. IEEE Trans. Neural Netw. 19, 1942–1955 (2008)

    Article  Google Scholar 

  19. Zhang, H., Wang, Z., Liu, D.: Robust exponential stability of cellular neural networks with multiple time varying delays. IEEE Trans. Circuits Syst. II 54, 730–734 (2007)

    Article  MathSciNet  Google Scholar 

  20. Wang, G., Cao, J.: Robust exponential stability analysis for stochastic genetic networks with uncertain parameters. Commun. Nonlinear Sci. Numer. Simul. 14, 3369–3378 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Kwon, O., Park, J., Lee, S.: On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays. Appl. Math. Comput. 197, 864–873 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  22. Kwon, O., Park, J., Lee, S.: On roust stability for uncertain neural networks with interval time-varying delays. IET Control Theory Appl. 2, 625–634 (2008)

    Article  MathSciNet  Google Scholar 

  23. Senan, S., Arik, S.: New results for global robust stability of bidirectional associative memory neural networks with multiple time delays. Chaos Solitons Fractals 41, 2106–2114 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Su, W., Chen, Y.: Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 14, 2293–2300 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang, L., Zhang, Y., Zhang, Z., Wang, Y.: LMI-based approach for global exponential robust stability for reaction-diffusion uncertain neural networks with time-varying delay. Chaos Solitons Fractals 41, 900–905 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Shao, J., Huang, T., Zhou, S.: An analysis on global robust exponential stability of neural networks with time-varying delays. Neurocomputing 72, 1993–1998 (2009)

    Article  Google Scholar 

  27. Zhang, R., Wang, L.: Global exponential robust stability of interval cellular neural networks with S-type distributed delays. Math. Comput. Model. 50, 380–385 (2009)

    Article  MATH  Google Scholar 

  28. Zhao, W., Zhu, Q.: New results of global robust exponential stability of neural networks with delays. Nonlinear Anal. Real World Appl. 11, 1190–1197 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zheng, C., Zhang, H., Wang, Z.: Novel delay-dependent criteria for global robust exponential stability of delayed cellular neural networks with norm-bounded uncertainties. Neurocomputing 72, 1744–1754 (2009)

    Article  Google Scholar 

  30. Zheng, C., Jing, X., Wang, Z., Feng, J.: Further results for robust stability of cellular neural networks with linear fractional uncertainty. Commun. Nonlinear Sci. Numer. Simul. (2009). doi:10.1016/j.cnsns.2009.11.007

    Google Scholar 

  31. Sheng, L., Yang, H.: Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays. Chaos Solitons Fractals 40, 2102–2113 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  32. Sheng, L., Yang, H.: Robust stability of uncertain Markovian jumping Cohen-Grossberg neural networks with mixed time-varying delays. Chaos Solitons Fractals 42, 2120–2128 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhang, J., Peng, S., Qiu, J.: Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties. Chaos Solitons Fractals 38(1), 160–167 (2008)

    Article  MathSciNet  Google Scholar 

  34. Chen, Y., Xue, A., Lu, R., Zhou, S.: On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations. Nonlinear Anal. 68, 2464–2470 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  35. Wu, H., Xue, X.: Stability analysis for neural networks with inverse Lipschizan neuron activations and impulses. Appl. Math. Model. 32, 2347–2359 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. Wu, H.: Global exponential stability of Hopfield neural networks with delays and inverse Lipschitz neuron activations. Nonlinear Anal., Real World Appl. 10, 2297–2306 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  37. Deimling, K.: Nonlinear Functional Analysis. Springer, Berlin (1985)

    MATH  Google Scholar 

  38. Miller, P., Michel, A.: Differential Equations. Academic Press, San Diego (1982)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Yanshan University, Qinhuangdao, 066001, China

    Huaiqin Wu, Feng Tao, Leijie Qin, Rui Shi & Lijun He

Authors
  1. Huaiqin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Leijie Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rui Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lijun He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huaiqin Wu.

Additional information

Supported by the Hebei Province Education Foundation of China (2009157).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, H., Tao, F., Qin, L. et al. Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions. Nonlinear Dyn 66, 479–487 (2011). https://doi.org/10.1007/s11071-010-9926-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-010-9926-9

Keywords

Search

Navigation