IEEE Trans Neural Netw Learn Syst. 2023 Mar;34(3):1578-1587. doi: 10.1109/TNNLS.2021.3105591. Epub 2023 Feb 28.
This article is concerned with the extended dissipativity of discrete-time neural networks (NNs) with time-varying delay. First, the necessary and sufficient condition on matrix-valued polynomial inequalities reported recently is extended to a general case, where the variable of the polynomial does not need to start from zero. Second, a novel Lyapunov functional with a delay-dependent Lyapunov matrix is constructed by taking into consideration more information on nonlinear activation functions. By employing the Lyapunov functional method, a novel delay and its variation-dependent criterion are obtained to investigate the effects of the time-varying delay and its variation rate on several performances, such as H performance, passivity, and l-l performance, of a delayed discrete-time NN in a unified framework. Finally, a numerical example is given to show that the proposed criterion outperforms some existing ones.
本文研究了时变时滞离散时间神经网络（NN）的扩展耗散性。首先，将最近报道的矩阵多项式不等式的必要和充分条件扩展到一般情况，其中多项式的变量不需要从零开始。其次，通过考虑更多关于非线性激活函数的信息，构造了一个具有时滞相关李雅普诺夫矩阵的新型李雅普诺夫函数。通过李雅普诺夫函数方法，得到了一个新的时滞及其变化率相关的判据，用于在统一框架内研究时变时滞及其变化率对时滞离散时间 NN 的几个性能的影响，如 H 性能、被动性和 l-l 性能。最后，通过一个数值例子表明，所提出的判据优于一些现有的判据。
