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Synchronization Analysis for Quaternion-Valued Delayed Neural Networks with Impulse and Inertia via a Direct Technique

Author

Listed:
  • Juan Yu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
    Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China)

  • Kailong Xiong

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China)

  • Cheng Hu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
    Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China)

Abstract

The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barbalat lemma and provides a powerful tool for the convergence analysis of discontinuous systems. To achieve synchronization, a constant gain-based control scheme and an adaptive gain-based control strategy are directly proposed for response quaternion-valued models. In the convergence analysis, a direct analysis method is developed to discuss the synchronization without using the separation technique or reduced-order transformation. In particular, some Lyapunov functionals, composed of the state variables and their derivatives, are directly constructed and some synchronization criteria represented by matrix inequalities are obtained based on quaternion theory. Some numerical results are shown to further confirm the theoretical analysis.

Suggested Citation

  • Juan Yu & Kailong Xiong & Cheng Hu, 2024. "Synchronization Analysis for Quaternion-Valued Delayed Neural Networks with Impulse and Inertia via a Direct Technique," Mathematics, MDPI, vol. 12(7), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:949-:d:1362396
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    References listed on IDEAS

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