Wang Hui-Ting, He Yong, Zhang Chuan-Ke
IEEE Trans Neural Netw Learn Syst. 2024 Feb;35(2):2875-2880. doi: 10.1109/TNNLS.2022.3184712. Epub 2024 Feb 5.
This article investigates the stability of delayed neural networks with large delays. Unlike previous studies, the original large delay is separated into several parts. Then, the delayed neural network is viewed as the switched system with one stable and multiple unstable subsystems. To effectively guarantee the stability of the considered system, the type-dependent average dwell time (ADT) is proposed to handle switches between any two sequences. Besides, multiple Lyapunov functions (MLFs) are employed to establish stability conditions. Adding more delayed state vectors increases the allowable maximum delay bound (AMDB), reducing the conservatism of stability criteria. A general form of the global exponential stability condition is put forward. Finally, a numerical example illustrates the effectiveness, and superiority of our method over the existing one.
本文研究了具有大时滞的时滞神经网络的稳定性。与以往的研究不同，原始的大时滞被分解为几个部分。然后，将时滞神经网络视为具有一个稳定子系统和多个不稳定子系统的切换系统。为了有效保证所考虑系统的稳定性，提出了依赖于类型的平均驻留时间（ADT）来处理任意两个序列之间的切换。此外，采用多个李雅普诺夫函数（MLF）来建立稳定性条件。增加更多的时滞状态向量会增加允许的最大时滞界（AMDB），从而降低稳定性判据的保守性。提出了全局指数稳定性条件的一般形式。最后，通过一个数值例子说明了我们方法的有效性以及相对于现有方法的优越性。
