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Global robust stability analysis of neural networks with discrete time delays

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  • Arik, Sabri

Abstract

Global robust convergence properties of continuous-time neural networks with discrete delays are studied. By using a Lyapunov functional, we derive a delay independent stability condition for the existence uniqueness and global robust asymptotic stability of the equilibrium point. The condition is in terms of the network parameters only and can be easily verified. It is also shown that the obtained result improves and generalizes a previously published result.

Suggested Citation

  • Arik, Sabri, 2005. "Global robust stability analysis of neural networks with discrete time delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1407-1414.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1407-1414
    DOI: 10.1016/j.chaos.2005.03.025
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    Cited by:

    1. Wu, Wei & Cui, Bao Tong & Huang, Min, 2007. "Global asymptotic stability of Cohen–Grossberg neural networks with constant and variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1355-1361.
    2. Sun, Yeong-Jeu, 2007. "Stability criterion for a class of descriptor systems with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 986-993.
    3. Xu, Jian & Chung, Kwok-Wai, 2009. "Dynamics for a class of nonlinear systems with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 28-49.
    4. Wang, Zidong & Lauria, Stanislao & Fang, Jian’an & Liu, Xiaohui, 2007. "Exponential stability of uncertain stochastic neural networks with mixed time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 62-72.
    5. Wang, Feifei & Chen, Diyi & Xu, Beibei & Zhang, Hao, 2016. "Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 329-338.
    6. 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.
    7. Sun, Yeong-Jeu, 2007. "Duality between observation and output feedback for linear systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 879-884.
    8. 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.
    9. Peng, Dezhong & Yi, Zhang, 2008. "Global convergence of an adaptive minor component extraction algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 550-561.
    10. Song, Qiankun, 2008. "Novel criteria for global exponential periodicity and stability of recurrent neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 720-728.
    11. Li, Chuandong & Chen, Jinyu & Huang, Tingwen, 2007. "A new criterion for global robust stability of interval neural networks with discrete time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 561-570.
    12. Wu, Wei & Cui, Bao Tong & Huang, Min, 2007. "Global asymptotic stability of delayed Cohen–Grossberg neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 872-877.
    13. Xiong, WeiLi & Xu, BaoGuo, 2008. "Some criteria for robust stability of Cohen–Grossberg neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1357-1365.
    14. Souza, Fernando O. & Palhares, Reinaldo M. & Ekel, Petr Ya., 2009. "Improved asymptotic stability analysis for uncertain delayed state neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 240-247.
    15. 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.
    16. Mak, K.L. & Peng, J.G. & Xu, Z.B. & Yiu, K.F.C., 2007. "A new stability criterion for discrete-time neural networks: Nonlinear spectral radius," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 424-436.
    17. Xiong, Wenjun & Ma, Deyi & Liang, Jinling, 2009. "Robust convergence of Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1176-1184.
    18. Ou, Ou, 2007. "Global robust exponential stability of delayed neural networks: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1742-1748.
    19. Wang, Zidong & Fang, Jian’an & Liu, Xiaohui, 2008. "Global stability of stochastic high-order neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 388-396.
    20. Lv, Jian Cheng & Yi, Zhang, 2007. "Convergence analysis of Chauvin’s PCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1562-1571.
    21. 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.
    22. Chang, Wenting & Sang, Hong & Guo, Liangdong & Wu, Libing & Dimirovski, Georgi M., 2024. "Integrated L∞ anti-disturbance synchronization control for switched neural networks with unknown delays," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    23. Gau, R.S. & Lien, C.H. & Hsieh, J.G., 2007. "Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1258-1267.
    24. Gao, Ming & Cui, Baotong, 2009. "Robust exponential stability of interval Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1914-1928.
    25. Zhou, Xiaobing & Wu, Yue & Li, Yi & Yao, Xun, 2009. "Stability and Hopf bifurcation analysis on a two-neuron network with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1493-1505.

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