Department of Computer Engineering, Faculty of Engineering Istanbul University-Cerrahpasa, Avcılar, Istanbul, Turkey.
Neural Netw. 2021 Oct;142:119-127. doi: 10.1016/j.neunet.2021.04.039. Epub 2021 May 7.
This research article considers the problem regarding global robust asymptotic stability of the general type of dynamical neural networks involving multiple constant time delays. Some new sufficient criteria are proposed for the existence, uniqueness and global asymptotic stability of the equilibrium point of this neural network model whose network parameters possess uncertainties. This paper will first address the existence and uniqueness problem for equilibrium points by utilizing the Homomorphic transformation theory. Secondly, by exploiting a novel Lyapunov functional candidate, the sufficient conditions for asymptotic stability of equilibrium points of this class of delayed neural networks will be established. The derived robust stability conditions are expressed independently of the constant time delay parameters and define some novel relationships among network parameters of the considered neural network. Thus, the applicability and validity of the obtained robust stability conditions for delayed-type neural networks can be easily tested. The comprehensive comparisons among the results of the current article and some of previously derived corresponding results will also be made by giving an illustrative numerical example.
这篇研究文章考虑了涉及多个常数时滞的一般类型动力神经网络的全局鲁棒渐近稳定性问题。针对具有不确定性网络参数的神经网络模型平衡点的存在性、唯一性和全局渐近稳定性，提出了一些新的充分判据。本文首先利用同态变换理论解决平衡点的存在唯一性问题。其次，通过利用一种新的李雅普诺夫泛函候选，建立了这类时滞神经网络平衡点渐近稳定性的充分条件。所得到的鲁棒稳定性条件与常数时滞参数无关，并定义了所考虑神经网络的网络参数之间的一些新关系。因此，可以很容易地检验所得到的时滞型神经网络鲁棒稳定性条件的适用性和有效性。通过给出一个说明性的数值例子，将本文的结果与之前得出的一些相应结果进行了全面比较。
