Global asymptotic stability of delayed neural networks with discontinuous neuron activations
Global asymptotic stability of delayed neural networks with discontinuous neuron activations
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DOI：
10.1016/j.neucom.2013.02.021
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发表时间：
2013-10
期刊：
影响因子：
6
通讯作者：
Jian Xiao;Z. Zeng;Wenwen Shen
中科院分区：
文献类型：
--
作者：
Jian Xiao;Z. Zeng;Wenwen Shen
在本文中，我们集成了一类具有不连续激活的延迟神经网络，这不应该是有界的或非减的。利用集值映射的Leray-Schauder定理建立了平衡点存在的条件。然后，利用生存定理证明了解的存在性。利用Lyapunov-Krasovskii稳定性理论研究了该网络的全局渐近稳定性。全局渐近稳定性的结果是以线性矩阵不等式形式给出的。所得结果推广了以往关于具有不连续激励的时滞神经网络全局稳定性的研究成果。
In this paper, we integrate a class of delayed neural networks with discontinuous activations, which are not supposed to be bounded or nondecreasing. Conditions of existence of an equilibrium point are established by means of the Leray–Schauder theorem of set-valued maps. Then, the existence of solutions is proved based on viability theorem. Furthermore, global asymptotical stability of the networks is studied by using Lyapunov–Krasovskii stability theory. The results of global asymptotical stability are in term of linear matrix inequality. The obtained results extend previous works on global stability of delayed neural networks with discontinues activations.