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<p>In this paper, a class of finite-time synchronization (FTS) and asymptotic synchronization issues of uncertain fractional-order quaternion-valued neural networks with time-varying delay are discussed, which closely simulate real-world applications. To tackle these issues, two efficient and straightforward controllers with time-varying delay are designed. The FTS criteria are derived by constructing a Lyapunov function and using algebraic condition, while asymptotic synchronization criterion is established by using linear matrix inequality (LMI) techniques. The algebraic technique utilizes the Razumikhin condition to guarantee synchronization and LMI technique employs the Schur complement to derive asymptotic synchronization conditions. Two numerical examples are provided to validate the effectiveness and accuracy of the proposed technique in achieving synchronization under the given conditions of uncertainty and time-varying delay.</p>

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Finite-time synchronization and asymptotic synchronization of uncertain fractional-order time delay quaternion-valued neural networks

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Muhammad Shakeel,
  • Xinge Liu,
  • Meilan Tang,
  • Shan Li,
  • Shuailei Zhang

摘要

In this paper, a class of finite-time synchronization (FTS) and asymptotic synchronization issues of uncertain fractional-order quaternion-valued neural networks with time-varying delay are discussed, which closely simulate real-world applications. To tackle these issues, two efficient and straightforward controllers with time-varying delay are designed. The FTS criteria are derived by constructing a Lyapunov function and using algebraic condition, while asymptotic synchronization criterion is established by using linear matrix inequality (LMI) techniques. The algebraic technique utilizes the Razumikhin condition to guarantee synchronization and LMI technique employs the Schur complement to derive asymptotic synchronization conditions. Two numerical examples are provided to validate the effectiveness and accuracy of the proposed technique in achieving synchronization under the given conditions of uncertainty and time-varying delay.