Zhang Xian-Ming, Han Qing-Long
Centre for Intelligent and Networked Systems and the School of Computing Sciences, Central Queensland University, Rockhampton, Qld. 4702, Australia.
IEEE Trans Neural Netw. 2009 Mar;20(3):533-9. doi: 10.1109/TNN.2009.2014160. Epub 2009 Feb 13.
This brief deals with the problem of global asymptotic stability for a class of delayed neural networks. Some new Lyapunov-Krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments, and choosing proper functionals with different weighting matrices corresponding to different segments in the Lyapunov-Krasovskii functionals. Then using these new Lyapunov-Krasovskii functionals, some new delay-dependent criteria for global asymptotic stability are derived for delayed neural networks, where both constant time delays and time-varying delays are treated. These criteria are much less conservative than some existing results, which is shown through a numerical example.
本文研究一类时滞神经网络的全局渐近稳定性问题。通过将延迟区间非均匀地划分为多个段，并在Lyapunov-Krasovskii泛函中为不同段选择具有不同加权矩阵的适当泛函，构造了一些新的Lyapunov-Krasovskii泛函。然后利用这些新的Lyapunov-Krasovskii泛函，推导了时滞神经网络全局渐近稳定性的一些新的时滞依赖准则，其中同时考虑了常时滞和变时滞。通过数值例子表明，这些准则比一些现有结果保守性要小得多。
