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Robustness Analysis of Global Exponential Stability of Recurrent Neural Networks in the Presence of Time Delays and Random Disturbances

机译：时滞和随机扰动下递归神经网络全局指数稳定性的鲁棒性分析

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摘要

In recent years, the global stability of recurrent neural networks (RNNs) has been investigated extensively. It is well known that time delays and external disturbances can derail the stability of RNNs. In this paper, we analyze the robustness of global stability of RNNs subject to time delays and random disturbances. Given a globally exponentially stable neural network, the problem to be addressed here is how much time delay and noise the RNN can withstand to be globally exponentially stable in the presence of delay and noise. The upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the RNNs to sustain global exponential stability. Moreover, we prove theoretically that, for any globally exponentially stable RNNs, if additive noises and time delays are smaller than the derived lower bounds arrived at here, then the perturbed RNNs are guaranteed to also be globally exponentially stable. Three numerical examples are provided to substantiate the theoretical results.
机译：近年来，对递归神经网络（RNN）的全局稳定性进行了广泛的研究。众所周知，时间延迟和外部干扰会破坏RNN的稳定性。在本文中，我们分析了受时间延迟和随机干扰影响的RNN全局稳定性的鲁棒性。给定一个全局指数稳定的神经网络，这里要解决的问题是，在存在延迟和噪声的情况下，RNN可以承受多少时间延迟和噪声。时延和噪声强度的上限通过对RNN使用超越方程来表征，以维持全局指数稳定性。此外，我们从理论上证明，对于任何全局指数稳定的RNN，如果加性噪声和时间延迟小于此处得出的下界，则可以保证被扰动的RNN也是全局指数稳定的。提供了三个数值示例来证实理论结果。

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