Department of Electrical and Electronics Engineering, Faculty of Engineering, Bursa Uludag University, Bursa, Turkey.
Neural Netw. 2019 May;113:20-27. doi: 10.1016/j.neunet.2019.01.017. Epub 2019 Feb 6.
The essential purpose of this work is to conduct an investigation into stability problem for the class of neutral-type Cohen-Grossberg neural networks including multiple time delays in states and multiple neutral delays in time derivative of states. By proposing an appropriate Lyapunov functional, a new sufficient criterion is derived for global asymptotic stability of neutral-type neural networks. The obtained stability criterion is independent of time delay and neutral delay parameters, and it is completely stated in terms of the elements of interconnection matrices and other network parameters. Thus, this newly presented stability condition can be validated by simply examining some algebraic equations establishing some relationships among the system parameters and matrices of the neutral-type neural system. A constructive example is presented to indicate applicability of the obtained sufficient stability condition. Since stability analysis of the class of neutral-type neural networks considered in this work has not been given much attention due to the difficulty of developing efficient mathematical techniques and methods enabling to conduct a stability analysis of such neutral-type neural systems, the criterion proposed in this paper can be considered as a leading stability result for neutral-type Cohen-Grossberg neural systems including multiple time and multiple neutral delays.
这项工作的基本目的是研究一类包含状态时滞和状态导数时滞的中立型 Cohen-Grossberg 神经网络的稳定性问题。通过提出一个合适的 Lyapunov 泛函，得到了中立型神经网络全局渐近稳定性的一个新的充分判据。所得的稳定性判据与时滞和中立时滞参数无关，完全用连接矩阵的元素和其他网络参数来表示。因此，通过简单地检查建立中立型神经网络系统参数和矩阵之间关系的一些代数方程，就可以验证这个新提出的稳定性条件。通过一个构造性的例子来说明所得到的充分稳定性条件的适用性。由于由于开发有效的数学技术和方法来对这类中立型神经网络系统进行稳定性分析存在困难，因此，这项工作中考虑的中立型神经网络的稳定性分析并没有得到太多关注。因此，本文提出的判据可以被认为是具有多个时滞和多个中立时滞的中立型 Cohen-Grossberg 神经网络系统的一个主要稳定性结果。
