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Exponential stability of neural networks with variable delays via LMI approach

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  • Yang, Haifeng
  • Chu, Tianguang
  • Zhang, Cishen

Abstract

This paper presents sufficient conditions for global asymptotic/exponential stability of neural networks with time-varying 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. Compared with some earlier work, our result does not require any restriction on the derivative of the delay function. Numerical example shows the efficiency and less conservatism of the present result.

Suggested Citation

  • Yang, Haifeng & Chu, Tianguang & Zhang, Cishen, 2006. "Exponential stability of neural networks with variable delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 133-139.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:1:p:133-139
    DOI: 10.1016/j.chaos.2005.08.134
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    Cited by:

    1. Singh, Vimal, 2009. "Remarks on estimating upper limit of norm of delayed connection weight matrix in the study of global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2013-2017.
    2. Qiu, Jiqing & Yang, Hongjiu & Zhang, Jinhui & Gao, Zhifeng, 2009. "New robust stability criteria for uncertain neural networks with interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 579-585.
    3. Cui, Shihua & Zhao, Tao & Guo, Jie, 2009. "Global robust exponential stability for interval neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1567-1576.
    4. Chu, Tianguang & Yang, Haifeng, 2007. "A note on exponential convergence of neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1538-1545.
    5. 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.
    6. Song, Qiankun & Wang, Zidong, 2008. "Neural networks with discrete and distributed time-varying delays: A general stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1538-1547.
    7. Zhao, Weirui & Yan, Anzhi, 2009. "Stability analysis of neural networks with both variable and unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 697-707.
    8. Dong, Ying & Sun, Chengjun, 2009. "Global existence of periodic solutions in a special neural network model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2249-2257.
    9. Zong, Guangdeng & Liu, Jia, 2009. "New delay-dependent global robust stability conditions for interval neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2954-2964.
    10. Qiu, Jiqing & Zhang, Jinhui & Wang, Jianfei & Xia, Yuanqing & Shi, Peng, 2008. "A new global robust stability criteria for uncertain neural networks with fast time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 360-368.
    11. Singh, Vimal, 2009. "Novel global robust stability criterion for neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 348-353.
    12. Park, Ju H., 2009. "Synchronization of cellular neural networks of neutral type via dynamic feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1299-1304.

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