College of Computer Science and Engineering, Chongqing University, Chongqing, 400044, China,
Cogn Neurodyn. 2008 Dec;2(4):363-70. doi: 10.1007/s11571-008-9058-9. Epub 2008 Sep 24.
This paper is concerned with the stability analysis for neural networks with interval time-varying delays and parameter uncertainties. An approach combining the Lyapunov-Krasovskii functional with the differential inequality and linear matrix inequality techniques is taken to investigate this problem. By constructing a new Lyapunov-Krasovskii functional and introducing some free weighting matrices, some less conservative delay-derivative-dependent and delay-derivative-independent stability criteria are established in term of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples show that the proposed criterion are effective and is an improvement over some existing results in the literature.
本文研究了具有区间时变时滞和参数不确定性的神经网络的稳定性分析。采用了一种结合李雅普诺夫-克拉索夫斯基泛函与微分不等式和线性矩阵不等式技术的方法来研究这个问题。通过构造一个新的李雅普诺夫-克拉索夫斯基泛函并引入一些自由加权矩阵，得到了一些基于线性矩阵不等式的更保守的时滞导数相关和时滞导数无关的稳定性准则。并且新准则适用于快速和缓慢时变时滞。三个数值例子表明，所提出的准则是有效的，并且优于文献中的一些已有结果。
