Mou Shaoshuai, Gao Huijun, Lam James, Qiang Wenyi
Department of ControlScience and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang Province 150001, China.
IEEE Trans Neural Netw. 2008 Mar;19(3):532-5. doi: 10.1109/TNN.2007.912593.
In this brief, the problem of global asymptotic stability for delayed Hopfield neural networks (HNNs) is investigated. A new criterion of asymptotic stability is derived by introducing a new kind of Lyapunov-Krasovskii functional and is formulated in terms of a linear matrix inequality (LMI), which can be readily solved via standard software. This new criterion based on a delay fractioning approach proves to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning. An example is provided to show the effectiveness and the advantage of the proposed result.
在本简报中，研究了时滞Hopfield神经网络（HNNs）的全局渐近稳定性问题。通过引入一种新型的Lyapunov-Krasovskii泛函，导出了一个渐近稳定性的新判据，并以线性矩阵不等式（LMI）的形式给出，该不等式可通过标准软件轻松求解。基于延迟分段方法的这一新判据被证明保守性要小得多，并且通过细化延迟分段可以显著降低保守性。给出了一个例子来说明所提结果的有效性和优势。
