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On networks over finite rings
Cheng, Daizhan1,2; Ji, Zhengping1,3
2022-09-01
Source PublicationJOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
ISSN0016-0032
Volume359Issue:14Pages:7562-7599
AbstractThe (control) networks over finite rings are proposed and their properties are investigated. Based on semi-tensor product (STP) of matrices, a set of algebraic equations are provided to verify whether a finite set with two binary operators is a ring. As an application, all rings with 4 elements are obtained. It is then shown that the STP-based technique developed for logical (control) networks are applicable to (control) networks over finite rings. A (control) sub-network over a proper ideal of the bearing ring is constructed. Certain properties are revealed, showing that a network over the ideal behaves like a subsystem over an invariant subspace. Product rings are then introduced, which provides a tool for both constructing product networks and decomposing complex networks. Finally, the representation of networks over finite rings is considered, which investigates how many finite networks can be expressed as networks over finite rings, showing that the technique developed in this paper is widely applicable. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
DOI10.1016/j.jfranklin.2022.07.039
Indexed BySCI
Language英语
Funding ProjectNNSF[62073315] ; NNSF[61074114] ; NNSF[61273013]
WOS Research AreaAutomation & Control Systems ; Engineering ; Mathematics
WOS SubjectAutomation & Control Systems ; Engineering, Multidisciplinary ; Engineering, Electrical & Electronic ; Mathematics, Interdisciplinary Applications
WOS IDWOS:000855295200015
PublisherPERGAMON-ELSEVIER SCIENCE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61023
Collection中国科学院数学与系统科学研究院
Corresponding AuthorCheng, Daizhan
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
2.Liaocheng Univ, Res Ctr Semitensor Prod Matrices, Lianocheng, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Cheng, Daizhan,Ji, Zhengping. On networks over finite rings[J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,2022,359(14):7562-7599.
APA Cheng, Daizhan,&Ji, Zhengping.(2022).On networks over finite rings.JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS,359(14),7562-7599.
MLA Cheng, Daizhan,et al."On networks over finite rings".JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 359.14(2022):7562-7599.
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