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A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays

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  • Chen, Yonghui
  • Xue, Yu
  • Yang, Xiaona
  • Zhang, Xian

Abstract

This paper mainly studies the global exponential stability in Lagrange sense (GESLS) of quaternion memristive neural networks (QMNNs) with leakage delays, unbounded distributed delays and time-varying discrete time delays. In the process of research, instead of traditional decomposition into real-valued memristive neural networks (RMNNs) or complex-valued memristive neural networks (CMNNs), we consider the QMNN as a whole, and then give a sufficient condition related to time delays to ensure that the considered QMNN is GESLS. An example is provided to illustrate validity of theoretical results obtained in the end. The method proposed in the present text has two merits: (1) According to the definition of GESLS directly, no Lyapunov–Krasovskii functional (LKF) is required, which avoids massive calculations and solutions of high-dimensional matrix inequalities; (2) It is available not only to QMNNs, but also to RMNNs and CMNNs.

Suggested Citation

  • Chen, Yonghui & Xue, Yu & Yang, Xiaona & Zhang, Xian, 2023. "A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    • Handle: RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322007056
    DOI: 10.1016/j.amc.2022.127633
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    References listed on IDEAS

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    1. Li, Ruoxia & Gao, Xingbao & Cao, Jinde, 2019. "Quasi-state estimation and quasi-synchronization control of quaternion-valued fractional-order fuzzy memristive neural networks: Vector ordering approach," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    2. Hanqi Shu & Qiankun Song & Jing Liang & Zhenjiang Zhao & Yurong Liu & Fuad E. Alsaadi, 2019. "Global exponential stability in Lagrange sense for quaternion-valued neural networks with leakage delay and mixed time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(4), pages 858-870, March.
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    4. Udhayakumar, K. & Rakkiyappan, R. & Li, Xiaodi & Cao, Jinde, 2021. "Mutiple ψ-type stability of fractional-order quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    5. Dong, Zeyu & Wang, Xin & Zhang, Xian, 2020. "A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 385(C).
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    8. Chen, Yonghui & Zhang, Xian & Xue, Yu, 2022. "Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 173-189.
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    Cited by:

    1. Yang, Liu & Ma, Weijun & Wang, Xin, 2024. "Lagrange stability and passivity in the mean square sense of discrete-time stochastic Markovian switched neural networks with time-varying mixed delays," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    2. Zhang, Hai & Chen, Xinbin & Ye, Renyu & Stamova, Ivanka & Cao, Jinde, 2023. "Adaptive quasi-synchronization analysis for Caputo delayed Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 49-65.
    3. Hua, Wentao & Wang, Yantao & Liu, Chunyan, 2024. "New method for global exponential synchronization of multi-link memristive neural networks with three kinds of time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 471(C).

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