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Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks

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  • Li, Hong-Li
  • Hu, Cheng
  • Zhang, Long
  • Jiang, Haijun
  • Cao, Jinde

Abstract

In this paper, robust finite-time synchronization (F-TS) issue is addressed for a class of uncertain fractional-order quaternion-valued neural networks by employing non-separation method instead of separation method. First, a general fractional differential inequality is developed to provide new insight into the research about finite-time stability and synchronization of fractional-order systems. Next, quaternion-valued feedback controller and quaternion-valued adaptive controller are designed. On the basis of the newly developed inequality, quaternion inequality techniques, together with the properties of fractional calculus and reduction to absurdity, some easily-verified algebraic criteria for robust F-TS are established, and the settling time for robust F-TS is explicitly reckoned, which depends on not only the controller parameters but also the initial values and order of the considered systems. Eventually, numerical results are provided to substantiate our robust F-TS criteria.

Suggested Citation

  • Li, Hong-Li & Hu, Cheng & Zhang, Long & Jiang, Haijun & Cao, Jinde, 2021. "Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004665
    DOI: 10.1016/j.amc.2021.126377
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    References listed on IDEAS

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    1. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    2. Du, Feifei & Lu, Jun-Guo, 2021. "New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    3. Zhang, Dian & Cheng, Jun & Cao, Jinde & Zhang, Dan, 2019. "Finite-time synchronization control for semi-Markov jump neural networks with mode-dependent stochastic parametric uncertainties," Applied Mathematics and Computation, Elsevier, vol. 344, pages 230-242.
    4. Hu, Taotao & He, Zheng & Zhang, Xiaojun & Zhong, Shouming, 2020. "Finite-time stability for fractional-order complex-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    5. Wu, Xifen & Bao, Haibo, 2020. "Finite time complete synchronization for fractional-order multiplex networks," Applied Mathematics and Computation, Elsevier, vol. 377(C).
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    Cited by:

    1. 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).
    2. Deng, Jie & Li, Hong-Li & Cao, Jinde & Hu, Cheng & Jiang, Haijun, 2023. "State estimation for discrete-time fractional-order neural networks with time-varying delays and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Li, Ruihong & Li, Xingxin & Gan, Qintao & Wu, Huaiqin & Cao, Jinde, 2023. "Finite time event-triggered consensus of variable-order fractional multi-agent systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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