Department of Management Information Systems, Faculty of Economics, Administrative and Social Sciences, Istanbul Nisantasi University, Maslak, Istanbul, Turkey.
Department of Mathematics, Faculty of Science, Istanbul University, 34134 Vezneciler, Istanbul, Turkey.
Neural Netw. 2023 May;162:186-198. doi: 10.1016/j.neunet.2023.02.040. Epub 2023 Mar 1.
Robust stability of different types of dynamical neural network models including time delay parameters have been extensively studied, and many different sets of sufficient conditions ensuring robust stability of these types of dynamical neural network models have been presented in past decades. In conducting stability analysis of dynamical neural systems, some basic properties of the employed activation functions and the forms of delay terms included in the mathematical representations of dynamical neural networks are of crucial importance in obtaining global stability criteria for dynamical neural systems. Therefore, this research article will examine a class of neural networks expressed by a mathematical model that involves the discrete time delay terms, the Lipschitz activation functions and possesses the intervalized parameter uncertainties. This paper will first present a new and alternative upper bound value of the second norm of the class of interval matrices, which will have an important impact on obtaining the desired results for establishing robust stability of these neural network models. Then, by exploiting wellknown Homeomorphism mapping theory and basic Lyapunov stability theory, we will state a new general framework for determining some novel robust stability conditions for dynamical neural networks possessing discrete time delay terms. This paper will also make a comprehensive review of some previously published robust stability results and show that the existing robust stability results can be easily derived from the results given in this paper.
已广泛研究了包括时滞参数在内的不同类型动力神经网络模型的鲁棒稳定性，并且在过去几十年中提出了许多确保这些类型动力神经网络模型鲁棒稳定性的不同充分条件集。在对动力神经网络系统进行稳定性分析时，所采用的激活函数的一些基本特性和动力神经网络数学表示中包含的延迟项的形式对于获得动力神经网络系统的全局稳定性准则至关重要。因此，本研究论文将研究一类由数学模型表示的神经网络，该模型涉及离散时间延迟项、李普希兹激活函数，并具有区间参数不确定性。本文首先提出了一类区间矩阵第二范数的新的替代上界值，这对于获得这些神经网络模型鲁棒稳定性所需的结果将有重要影响。然后，通过利用著名的同胚映射理论和基本李雅普诺夫稳定性理论，我们将为具有离散时间延迟项的动力神经网络确定一些新的鲁棒稳定性条件的新的一般框架。本文还将对一些以前发表的鲁棒稳定性结果进行全面回顾，并表明可以从本文给出的结果中轻松推导出现有的鲁棒稳定性结果。
