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Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach

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  • Li, Chuandong
  • Liao, Xiaofeng
  • Zhang, Rong

Abstract

For bi-directional associative memory (BAM) neural networks (NNs) with different constant or time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are investigated in this paper. An approach combining the Lyapunov–Krasovskii functional with the linear matrix inequality (LMI) is taken to study the problems, which provide bounds on the interconnection matrix and the activation functions, so as to guarantee the system’s exponential stability. Some criteria for the exponential stability, which give information on the delay-dependent property, are derived. The results obtained in this paper provide one more set of easily verified guidelines for determining the exponential stability of delayed BAM (DBAM) neural networks, which are less conservative and less restrictive than the ones reported so far in the literature. Some typical examples are presented to show the application of the criteria obtained in this paper.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:4:p:1119-1134
    DOI: 10.1016/j.chaos.2004.09.052
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    Citations

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    Cited by:

    1. 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.
    2. Guan, Zhi-Hong & Zhang, Hao & Yang, Shuang-Hua, 2008. "Robust passive control for Internet-based switching systems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 479-486.
    3. Yan, Huaicheng & Huang, Xinhan & Wang, Min & Zhang, Hao, 2007. "Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 997-1005.
    4. Sheng, Li & Yang, Huizhong, 2009. "Novel global robust exponential stability criterion for uncertain BAM neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2102-2113.
    5. Zhou, Tiejun & Liu, Yuehua & Li, Xiaoping & Liu, Yirong, 2009. "A new criterion to global exponential periodicity for discrete-time BAM neural network with infinite delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 332-341.
    6. Yan, Huaicheng & Huang, Xinhan & Wang, Min & Zhang, Hao, 2008. "New delay-dependent stability criteria of uncertain linear systems with multiple time-varying state delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 157-165.
    7. Yang, Degang & Liao, Xiaofeng & Hu, Chunyan & Wang, Yong, 2009. "New delay-dependent exponential stability criteria of BAM neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1679-1697.
    8. Wang, Huiwei & Song, Qiankun & Duan, Chengjun, 2010. "LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 837-850.
    9. Chen, Jun & Cui, Baotong, 2008. "Impulsive effects on global asymptotic stability of delay BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1115-1125.
    10. Liu, Hailin & Chen, Guohua, 2007. "Delay-dependent stability for neural networks with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 171-177.
    11. Zhao, Hongyong & Ding, Nan, 2007. "Dynamic analysis of stochastic bidirectional associative memory neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1692-1702.
    12. Huang, Tingwen & Li, Chuandong & Chen, Goong, 2007. "Stability of Cohen–Grossberg neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 992-996.
    13. 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.

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