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Admissible Delay Upper Bounds for Global Asymptotic Stability of Neural Networks With Time-Varying Delays.具有时变延迟的神经网络全局渐近稳定性的容许延迟上界
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Multistability Analysis of Quaternion-Valued Neural Networks With Time Delays.具有时滞的四元数神经网络的多重稳定性分析
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New Lyapunov-Krasovskii functionals for global asymptotic stability of delayed neural networks.用于时滞神经网络全局渐近稳定性的新型Lyapunov-Krasovskii泛函
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基于一类扩展Lyapunov-Razumikhin方法的时滞四元数神经网络的全局有限时间稳定性

Global finite-time stability of delayed quaternion-valued neural networks based on a class of extended Lyapunov-Razumikhin methods.

作者信息

Li Chengsheng, Cao Jinde, Kashkynbayev Ardak

机构信息

School of Mathematics, Southeast University, Nanjing, 210096 China.

Research Center for Complex Systems and Network Sciences, and School of Mathematics, Southeast University, Nanjing, 210096 China.

出版信息

Cogn Neurodyn. 2023 Jun;17(3):729-739. doi: 10.1007/s11571-022-09860-9. Epub 2022 Aug 3.

DOI:10.1007/s11571-022-09860-9
PMID:37265657
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10229506/
Abstract

In this paper, a class of global finite-time stability problem for quaternion-valued neural networks with time-varying delays are investigated by adopting an extended modification Lyapunov-Razumikhin (L-R) method and a new upper bounds estimation of system solution in terms of convergence rate was obtained. Firstly, a new extended method of L-R is proposed to solve the general difficulty to find a proper Lyapunov functional. Then, a new suitable controller is designed, the new conditions of inequalities global finite-time stability are obtained via combining with the former proposed L-R method in the separated real-valued system. Finally, for purpose of verifying the availability of the theorem presented, two given illustrative examples are shown.

摘要

本文采用扩展的修正Lyapunov-Razumikhin（L-R）方法研究了一类具有时变延迟的四元数神经网络的全局有限时间稳定性问题，并得到了基于收敛速率的系统解的新的上界估计。首先，提出了一种新的L-R扩展方法，以解决寻找合适的Lyapunov泛函这一普遍难题。然后，设计了一种新的合适控制器，通过与之前在分离实值系统中提出的L-R方法相结合，得到了不等式全局有限时间稳定性的新条件。最后，为了验证所提出定理的有效性，给出了两个示例。