Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays
Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays
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DOI：
10.1016/j.neunet.2003.08.007
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发表时间：
2004-04
期刊：
影响因子：
--
通讯作者：
Jinde Cao;Jun Wang
中科院分区：
文献类型：
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作者：
Jinde Cao;Jun Wang
本文研究了一类一般时滞神经网络的绝对指数稳定性，它要求激活函数部分Lipschitz连续且单调非减，但不一定可微或有界。利用时滞Halanay型不等式和Lyapunov函数，给出了具有可加对角稳定互联矩阵的时滞神经网络平衡点是否绝对指数稳定的三个新的充分条件。稳定性判据也适用于时滞优化神经网络和时滞细胞神经网络，它们的激活函数往往是不可微的或无界的。这里的结果回答了一个问题：如果没有任何时滞的神经网络是绝对指数稳定的，那么在什么附加条件下，带时滞的神经网络也是绝对指数稳定的。
This paper investigates the absolute exponential stability of a general class of delayed neural networks, which require the activation functions to be partially Lipschitz continuous and monotone nondecreasing only, but not necessarily differentiable or bounded. Three new sufficient conditions are derived to ascertain whether or not the equilibrium points of the delayed neural networks with additively diagonally stable interconnection matrices are absolutely exponentially stable by using delay Halanay-type inequality and Lyapunov function. The stability criteria are also suitable for delayed optimization neural networks and delayed cellular neural networks whose activation functions are often nondifferentiable or unbounded. The results herein answer a question: if a neural network without any delay is absolutely exponentially stable, then under what additional conditions, the neural networks with delay is also absolutely exponentially stable.