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Globally exponential stabilization of neural networks with mixed time delays via impulsive control

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  • Wei, Linna
  • Chen, Wu-Hua
  • Huang, Ganji

Abstract

The impulsive stabilization problem of neural networks with discrete time-varying delays and unbounded continuously distributed delays is considered. By using impulse-time-dependent Lyapunov function-based techniques to capture the hybrid structure characteristics of the considered impulsive neural networks, two novel global exponential stability criteria are obtained in terms of linear matrix inequalities, which are capable of dealing with the case where both the continuous and discrete dynamics are unstable. When the original continuous-time delayed neural networks are not stable, sufficient conditions are developed for the design of exponentially stable linear impulsive state feedback controllers. Four numerical examples are given to illustrate the less conservatism and effectiveness of the proposed results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:260:y:2015:i:c:p:10-26
    DOI: 10.1016/j.amc.2015.03.043
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    References listed on IDEAS

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    1. Song, Qiankun & Wang, Zidong, 2008. "Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3314-3326.
    2. 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.
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    Cited by:

    1. Li, Xian-Feng & Chu, Yan-Dong & Leung, Andrew Y.T. & Zhang, Hui, 2017. "Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 24-30.
    2. Yujuan Tian & Yuhan Yin & Fei Wang & Kening Wang, 2022. "Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    3. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Chen, Dazhao & Zhang, Zhengqiu, 2022. "Finite-time synchronization for delayed BAM neural networks by the approach of the same structural functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Rakkiyappan, R. & Velmurugan, G. & Nicholas George, J. & Selvamani, R., 2017. "Exponential synchronization of Lur’e complex dynamical networks with uncertain inner coupling and pinning impulsive control," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 217-231.

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