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New delay-dependent global asymptotic stability criteria of delayed BAM neural networks

Author

Listed:
  • Yang, Degang
  • Hu, Chunyan
  • Chen, Yong
  • Wei, Pengcheng
  • Yang, Huaqian

Abstract

In this paper, the global asymptotic stability of BAM neural networks with delays is investigated by utilizing Lyapunov functional method and the linear matrix inequality (LMI) technique. Distinct difference from other analytical approaches lies in “linearization” of the neural network model, by which the considered neural network model is transformed into a linear system. Then, a process, which is called parameterized first-order model transformation, is used to transform the linear system. Novel criteria for global asymptotic stability of the unique equilibrium point of BAM neural networks with delays are obtained. The results are related to the size of delays. The obtained results are less conservative and restrictive than those established in the earlier references. A numerical example is given to show the effectiveness of our proposed method.

Suggested Citation

  • Yang, Degang & Hu, Chunyan & Chen, Yong & Wei, Pengcheng & Yang, Huaqian, 2009. "New delay-dependent global asymptotic stability criteria of delayed BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 854-864.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:854-864
    DOI: 10.1016/j.chaos.2009.02.018
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    References listed on IDEAS

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    1. Park, Ju H., 2006. "A novel criterion for global asymptotic stability of BAM neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 446-453.
    2. 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.
    3. Lou, Xu Yang & Cui, Bao Tong, 2006. "Global asymptotic stability of delay BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 1023-1031.
    4. Yaping Ren & Yongkun Li, 2007. "Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-8, April.
    5. Wang, Hui & Liao, Xiaofeng & Li, Chuandong, 2007. "Existence and exponential stability of periodic solution of BAM neural networks with impulse and time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1028-1039.
    6. Li, Chuandong & Liao, Xiaofeng & Zhang, Rong, 2005. "Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1119-1134.
    7. Huang, Xia & Cao, Jinde & Huang, De-Shuang, 2005. "LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 885-898.
    8. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
    9. Kaslik, E. & Balint, St., 2007. "Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1245-1253.
    10. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
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