基于Lyapunov-Krasovskii泛函的时变时滞神经网络稳定性分析
Stability Analysis for Neural Networks with Time-Varying Delays Based on Lyapunov-Krasovskii Functional Approach
DOI: 10.12677/CSA.2022.1212279, PDF,   
作者: 刘新英：天津工业大学计算机科学与技术学院，天津;天津市自主智能技术与系统重点实验室，天津
关键词: 李雅普诺夫–克拉索夫斯基泛函；容许时滞上限；全局渐进稳定性；神经网络；Lyapunov-Krasovskii Functional； Admissible Delay Upper Bounds； Global Asymptotic Stability； Neural Networks
摘要: 本文研究了一类时变时滞神经网络的全局渐进稳定性问题。李雅普诺夫稳定性理论为分析具有时变时滞的神经网络的鲁棒性能提供了有力的工具。基于这一理论，在本文中首先选择了一个合适的增广型Lyapunov-Krasovskii泛函，该泛函中引入了一些延迟积分项和松弛矩阵，并融合一些其它的时滞信息、系统信息因素等，令各类信息间的关联程度更加紧密，增大最大可允许时延的上限，使得系统的稳定性结论的保守性降低。其次，通过对该泛函求导后出现的二次积分项进行适当的放缩来降低系统稳定性判据的保守性，本文中使用了一个新的积分不等式来估计该泛函导数中的二次积分项，建立了时变时滞神经网络全局渐进稳定性的新判据。最后，通过数值例子对本文所提结论的有效性进行了验证。
Abstract: This paper is concerned with the problem of global asymptotic stability for a class of neural net-works with time-varying delays. The Lyapunov stability theory provides a powerful tool for analyzing the robust performance of neural networks with time-varying delays. Based on this theory, first, by introducing some delay-product-type terms and relaxation matrices, a new augmented LKF is constructed, which contains more information on time-varying delay and system states, so that the correlation between all kinds of information is closer, the admissible delay upper bounds is increased, and the conservatism of the stability criteria of the system is reduced. Second, the quadratic integral term appearing after the derivative of LKF is scaled appropriately to reduce the conservatism of the stability criterion. A new integral inequality is used to estimate the quadratic integral term in the derivative of LKF, and a new criterion of global asymptotic stability of neural net-works with time-varying delays is established. Finally, numerical examples are employed to illustrate the effectiveness of the proposed method.
文章引用：刘新英. 基于Lyapunov-Krasovskii泛函的时变时滞神经网络稳定性分析[J]. 计算机科学与应用, 2022, 12(12): 2754-2762. https://doi.org/10.12677/CSA.2022.1212279

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