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LMI conditions for stability of neural networks with distributed delays

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  • Yang, Haifeng
  • Chu, Tianguang

Abstract

This paper presents new sufficient conditions for global asymptotic stability of neural networks with discrete and distributed delays. By using appropriate Lyapunov–Krasovskii functionals, we derive stability conditions in terms of linear matrix inequalities (LMIs). This is convenient for numerically checking the system stability using the powerful MATLAB LMI Toolbox. Moreover, existing conditions are mostly based on certain diagonal dominance or M matrix conditions on weight matrices of the neural networks, which only make use of absolute values of the weights and ignore their sign, and hence are somewhat conservative. The LMI-based results obtained here can get rid of this disadvantage and give less conservative stability conditions. We illustrate this with numerical examples.

Suggested Citation

  • Yang, Haifeng & Chu, Tianguang, 2007. "LMI conditions for stability of neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 557-563.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:557-563
    DOI: 10.1016/j.chaos.2006.03.072
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    References listed on IDEAS

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    1. Song, Qiankun & Zhao, Zhenjiang, 2005. "Global dissipativity of neural networks with both variable and unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 393-401.
    2. Singh, Vimal, 2006. "Simplified LMI condition for global asymptotic stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 470-473.
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    Cited by:

    1. Park, Ju H., 2008. "On global stability criterion of neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 444-449.
    2. Xu, Liguang & Xu, Daoyi, 2009. "Exponential p-stability of impulsive stochastic neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 263-272.
    3. Rakkiyappan, R. & Balasubramaniam, P., 2009. "LMI conditions for stability of stochastic recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1688-1696.
    4. Tian, Junkang & Xu, Dongsheng, 2009. "New asymptotic stability criteria for neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1916-1922.
    5. Wei, Linna & Chen, Wu-Hua & Huang, Ganji, 2015. "Globally exponential stabilization of neural networks with mixed time delays via impulsive control," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 10-26.

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