Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain
Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain
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DOI：
10.1109/tnn.2005.852862
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发表时间：
2005-11
影响因子：
--
通讯作者：
M. Forti;P. Nistri;D. Papini
中科院分区：
文献类型：
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作者：
M. Forti;P. Nistri;D. Papini
本文介绍了一类神经网络，其神经元互连具有任意常数时滞，神经元激活属于不连续单调递增且（可能）无界函数的集合。激活中的不连续性是神经元放大器的增益非常高并且趋于无穷大的情况的理想模型，而延迟考虑了神经元放大器的有限切换速度或有限信号传播速度。众所周知，与高增益非线性相结合的延迟是潜在不稳定性的特别有害的来源。本文的目标是挑选出一个子类的考虑不连续的神经网络的稳定性，而不是不敏感的延迟的存在。更准确地说，条件下，有一个唯一的平衡点的神经网络，这是全局指数稳定的状态，具有已知的收敛速度。这些条件是容易检验的，并且与时滞无关。此外，在有限时间内的状态和输出的全局收敛性进行了研究。在这样做时，新的有趣的动力学现象突出的情况下，没有延迟，这使得研究收敛在有限时间显着更加困难。所得结果推广了以往关于具有Lipschitz连续神经元激活的时滞神经网络和具有不连续神经元激活但不含时滞的神经网络的全局稳定性的工作.
This paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections, and neuron activations belonging to the set of discontinuous monotone increasing and (possibly) unbounded functions. The discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity, while the delay accounts for the finite switching speed of the neuron amplifiers, or the finite signal propagation speed. It is known that the delay in combination with high-gain nonlinearities is a particularly harmful source of potential instability. The goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay. More precisely, conditions are given under which there is a unique equilibrium point of the neural network, which is globally exponentially stable for the states, with a known convergence rate. The conditions are easily testable and independent of the delay. Moreover, global convergence in finite time of the state and output is investigated. In doing so, new interesting dynamical phenomena are highlighted with respect to the case without delay, which make the study of convergence in finite time significantly more difficult. The obtained results extend previous work on global stability of delayed neural networks with Lipschitz continuous neuron activations, and neural networks with discontinuous neuron activations but without delays.