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Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field
Zhang, Dandan1; Kou, Kit Ian2; Liu, Yang1,3; Cao, Jinde3
2017-10
Source PublicationNEURAL NETWORKS
ISSN0893-6080
Volume94Pages:55-66
Abstract

In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronous time delays is investigated in quaternion field. Due to the non-commutativity of quaternion multiplication resulting from Hamilton rules: ij = -ji = k, jk = -kj = i, ki = -ik = j, ijk = i(2) = j(2) = k(2) = -1, the QVNN is decomposed into four real-valued systems, which are studied separately. The exponential convergence is proved directly accompanied with the existence and uniqueness of the equilibrium point to the consider systems. Combining with the generalized infinity-norm and Cauchy convergence property in the quaternion field, some sufficient conditions to guarantee the stability are established without using any Lyapunov-Krasovskii functional and linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the results. (C) 2017 Elsevier Ltd. All rights reserved.

KeywordGlobal Exponential Stability Quaternion-valued Neural Network Asynchronous Time Delay Linear Matrix Inequality
DOIhttps://doi.org/10.1016/j.neunet.2017.06.014
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Neurosciences & Neurology
WOS SubjectComputer Science, Artificial Intelligence ; Neurosciences
WOS IDWOS:000410973300006
PublisherPERGAMON-ELSEVIER SCIENCE LTD
The Source to ArticleWOS
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Cited Times [WOS]:31   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorLiu, Yang
Affiliation1.College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, China
2.Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau, China
3.School of Mathematics, Southeast University, Nanjing, China
Recommended Citation
GB/T 7714
Zhang, Dandan,Kou, Kit Ian,Liu, Yang,et al. Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field[J]. NEURAL NETWORKS,2017,94:55-66.
APA Zhang, Dandan,Kou, Kit Ian,Liu, Yang,&Cao, Jinde.(2017).Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field.NEURAL NETWORKS,94,55-66.
MLA Zhang, Dandan,et al."Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field".NEURAL NETWORKS 94(2017):55-66.
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