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On stability and event trigger control of fractional neural networks by fractional non-autonomous Halanay inequalities

Author

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  • Wang, Feng-Xian
  • Zhang, Jie
  • Shu, Yan-Jun
  • Liu, Xin-Ge

Abstract

This paper studies the stability and control of fractional neural networks by Halanay inequality technique. Based on the fractional comparison principle and supremum and infimum principle, a novel fractional non-autonomous Halanay inequality is developed. The fractional non-autonomous Halanay inequality is in a form of integral, which considers the global nature of the system parameters and reduces estimation error. By combining the Halanay inequality with a maximum auxiliary function, an asymptotically stable discriminant condition for fractional Hopfield time-delay neural networks is established in an algebraic form. Moreover, event trigger control for fractional neural networks is studied. Low network bandwidth costs and high control efficiency are guaranteed by a Mittag-Leffler type event-triggered mechanism. Then, a discriminant condition on the event trigger control for fractional neural networks is established. The advantages of the proposed methods are demonstrated by three numerical examples.

Suggested Citation

  • Wang, Feng-Xian & Zhang, Jie & Shu, Yan-Jun & Liu, Xin-Ge, 2023. "On stability and event trigger control of fractional neural networks by fractional non-autonomous Halanay inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923003193
    DOI: 10.1016/j.chaos.2023.113418
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    References listed on IDEAS

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    1. Huang, Conggui & Wang, Fei & Zheng, Zhaowen, 2021. "Exponential stability for nonlinear fractional order sampled-data control systems with its applications," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Liu, Xiang & Wang, Peiguang & Anderson, Douglas R., 2022. "On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
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    Cited by:

    1. Wang, Huanan & Huang, Chengdai & Liu, Heng & Cao, Jinde, 2023. "Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer’s rule," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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