Hu Liang, Gao Huijun, Zheng Wei Xing
Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China.
Neural Netw. 2008 Dec;21(10):1458-63. doi: 10.1016/j.neunet.2008.09.002. Epub 2008 Sep 11.
In this paper, the asymptotic stability is investigated for a class of cellular neural networks with interval time-varying delay (that is, 0<h1<dt<h2). By introducing a novel Lyapunov functional with the idea of partitioning the lower bound h1 of the time-varying delay, a new criterion of asymptotic stability is derived in terms of a linear matrix inequality (LMI), which can be efficiently solved via standard numerical software. The criterion proves to be less conservative than most of the existing results, and the conservatism could be notably reduced by thinning the delay partitioning. Two examples are provided to demonstrate the less conservatism and effectiveness of the proposed stability conditions.
本文研究了一类具有区间时变延迟（即0 < h1 < dt < h2）的细胞神经网络的渐近稳定性。通过引入一种新颖的李雅普诺夫泛函，并采用划分时变延迟下界h1的思想，基于线性矩阵不等式（LMI）导出了一个新的渐近稳定性判据，该判据可通过标准数值软件有效求解。结果表明，该判据比大多数现有结果的保守性更低，并且通过细化延迟划分可显著降低保守性。给出了两个例子以说明所提出的稳定性条件的低保守性和有效性。
