This article deals with the issue of input-to-state stabilization for recurrent neural networks with delay and external disturbance. The goal is to design a suitable weight-learning law to make the considered network input-to-state stable with a predefined -gain. Based on the solution of linear matrix inequalities, two schemes for the desired learning law are presented via using decay-rate-dependent and decay-rate-independent Lyapunov functionals, respectively. It is shown that, in the absence of external disturbance, the proposed learning law also guarantees the exponential stability of the network. To illustrate the applicability of the present weight-learning law, two numerical examples with simulations are given.

中文翻译：

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具有延迟和干扰的循环神经网络的输入状态学习

本文涉及具有延迟和外部干扰的循环神经网络的输入到状态稳定问题。目标是设计一个合适的权重学习法则，使所考虑的网络输入到状态稳定并具有预定义的增益。基于线性矩阵不等式的解，分别通过使用衰减率相关和衰减率无关的李雅普诺夫泛函提出了所需学习规律的两种方案。结果表明，在没有外部干扰的情况下，所提出的学习规律也保证了网络的指数稳定性。为了说明当前权重学习定律的适用性，给出了两个带有模拟的数值例子。