Letters: Global asymptotic stability of delayed neural networks with discontinuous neuron activations

Authors:
Jian Xiao;Zhigang Zeng;Wenwen Shen
Affiliations:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China and Key Laboratory of Image Processing and Intelligent Control of Education Minist ...;Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China and Key Laboratory of Image Processing and Intelligent Control of Education Minist ...;Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China and Key Laboratory of Image Processing and Intelligent Control of Education Minist ...
Venue:
Neurocomputing
Year:
2013

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Abstract

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.