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Pure Mathematics 2025
具有脉冲和时滞的四元数神经网络的输入到状态稳定性
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Abstract:
本文主要研究具有脉冲和时滞的四元数神经网络(QVNN)的输入到状态稳定(ISS)。首先，由于四元数乘法不适用于交换律，所以我们将四元数神经网络分解为四个实值神经网络来进行分析，然后通过比较原理和平均脉冲间隔方法，以及利用Lyapunov-Krasovskii函数和一些矩阵不等式，提出了一些充分的条件，以确保所考虑的系统是输入到状态稳定(ISS)。最后，我们给出了一个数值模拟例子及其仿真图来证明理论结果的正确性和有效性。
In this paper, the input-to-state stability of quaternion-valued neural networks (QVNN) with impulses and time delay is investigated. First of all, in virtue of the quaternion multiplication is not suitable for commutative law, QVNN is resolved into four real-valued neural networks (RVNNs). With the help of the comparison principle and average impulse interval approach, and making use of a Lyapunov function and some inequalities, we obtain sufficient conditions to assure the considered system is ISS. Finally, one numerical example and their simulations are given to show the correctness and effectiveness of our theoretical results.
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