The Research Institute of Automation, Qufu Normal University, Rizhao, 276826, China.
The Research Institute of Automation, Qufu Normal University, Rizhao, 276826, China.
ISA Trans. 2018 Sep;80:35-42. doi: 10.1016/j.isatra.2018.05.016. Epub 2018 Jul 17.
This paper is concerned with a new Lyapunov-Krasovskii functional (LKF) approach to the stability for neural networks with time-varying delays. The LKF has two features: First, it can make full use of the information of the activation function. Second, it employs the information of the maximal delayed state as well as the instant state and the delayed state. When estimating the derivative of the LKF we employ a new technique that has two characteristics: One is that Wirtinger-based integral inequality and an extended reciprocally convex inequality are jointly employed; the other is that the information of the activation function is used as much as we can. Based on Lyapunov stability theory, a new stability result is obtained. Finally, three examples are given to illustrate the stability result is less conservative than some recently reported ones.
本文针对时变时滞神经网络的稳定性问题，研究了一种新的李雅普诺夫-克拉索夫斯基泛函（LKF）方法。该 LKF 具有两个特点：首先，它可以充分利用激活函数的信息。其次，它利用了最大时滞状态的信息以及即时状态和时滞状态的信息。在估计 LKF 的导数时，我们采用了一种新技术，该技术具有两个特点：一是联合使用基于 Wirtinger 的积分不等式和扩展的互凸不等式；二是尽可能地利用激活函数的信息。基于李雅普诺夫稳定性理论，得到了一个新的稳定性结果。最后，给出了三个实例来说明该稳定性结果比最近报道的一些结果更保守。
