IEEE Trans Cybern. 2022 Jun;52(6):5356-5366. doi: 10.1109/TCYB.2020.3031087. Epub 2022 Jun 16.
The stability of neural networks with a time-varying delay is studied in this article. First, a relaxed Lyapunov-Krasovskii functional (LKF) is presented, in which the positive-definiteness requirement of the augmented quadratic term and the delay-product-type terms are set free, and two double integral states are augmented into the single integral terms at the same time. Second, a new negative-definiteness determination method is put forward for quadratic functions by utilizing Taylor's formula and the interval-decomposition approach. This method encompasses the previous negative-definiteness determination approaches and has less conservatism. Finally, the proposed LKF and the negative-definiteness determination method are applied to the stability analysis of neural networks with a time-varying delay, whose advantages are shown by two numerical examples.
本文研究了时变时滞神经网络的稳定性。首先，提出了一个松弛的 Lyapunov-Krasovskii 泛函（LKF），其中放宽了增广二次项和时滞积项的正定要求，同时将两个双积分状态增广到单个积分项中。其次，通过利用泰勒公式和区间分解方法，提出了一种新的二次函数负定性判定方法。该方法包含了以前的负定性判定方法，具有更小的保守性。最后，将所提出的 LKF 和负定性判定方法应用于时变时滞神经网络的稳定性分析，通过两个数值例子展示了其优势。
