Abstract
In this paper, stochastic Hopfield neural networks with time-varying delays are investigated based on Lyapunov-krasovskii functional approach and linear matrix inequality(LMI) technique. The proposed criterion is expressed in terms of linear matrix inequality(LMI)and is less conservative than some existing ones and can be effectively solved by Matlab LMI toolbox. A numerical example that confirms the theoretical result is also presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Singh, V.: A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Network 15, 223–225 (2004)
Arik, S.: An analysis of exponential atability of delay neural networks with time varing delays. Neural Network 17, 1027–1031 (2004)
Cao, J., Yuan, K., Li, H.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Network 17, 1646–1651 (2006)
Liu, X., Jiang, N.: Robust stability analysis of generalized neural networks with multiple discrete delays and multiple distributed delays. Neurocomuting 72, 1789–1796 (2009)
Blythe, S., Mao, X., Liao, X.: Stability of stochastic delay neural networks. Journal of the Franklin Institute 338, 481–495 (2001)
Liao, X., Mao, X.: Stability of stochastic neural networks. Neural, Parallel Scientific Computations 4, 205–224 (1996)
Liao, X., Mao, X.: Exponential stability and instability of stochastic neural networks. Stochastic Analysis and Applications 14, 165–185 (1996)
Huang, H., Ho, D., Lam, J.: Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Trans. Circuits Syst. 52, 251–255 (2005)
Lou, X., Cui, B.: Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameter. Journal of Mathematical Analysis and Applications 328, 316–326 (2007)
Wang, Z.: Robust stability for stochastic Hopfield neural networks with time delay. Nonlinear Analysis, Real-world Application 7, 1119–1128 (2006)
Lou, X., Cui, B.: Stochastic Robust Stability of Markovian Jump Nonlinear Uncertain Neural Networks with Wiener Process. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 165–171. Springer, Heidelberg (2006)
Cao, J., Huang, D., Qu, Y.: Global robust stability of delayed recurrent neural networks. Chaos, Solitons Franctals 123, 221–229 (2005)
Cao, J., Chen, T.: Globally exponentially robust stability and periodicity of delay neural networks. Chaos, Solitons Fractals 22, 957–963 (2004)
Xu, S., Lam, J., Ho, D.: Novel global robust stability criteria for interval neural networks with multiple time-varying delays. Phys. Lett. A 342, 322–331 (2005)
Shen, T., Zhang, Y.: Improve global robust stability criteria for delayed neural networks. IEEE Trans. Circuits Syst. 54, 715–719 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, X., Wang, M. (2012). Novel Robust Stability Criteria for Stochastic Hopfield Neural Network with Time-Varying Delays. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34487-9_57
Download citation
DOI: https://doi.org/10.1007/978-3-642-34487-9_57
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34486-2
Online ISBN: 978-3-642-34487-9
eBook Packages: Computer ScienceComputer Science (R0)