On networks over finite rings

doi:10.1016/j.jfranklin.2022.07.039

	On networks over finite rings
	Cheng, Daizhan 1,2; Ji, Zhengping 1,3
刊名	JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
	2022-09-01
卷号	359 期号:14 页码:7562-7599
ISSN号	0016-0032
DOI	10.1016/j.jfranklin.2022.07.039
英文摘要	The (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.
资助项目	NNSF[62073315] ; NNSF[61074114] ; NNSF[61273013]
WOS研究方向	Automation & Control Systems ; Engineering ; Mathematics
语种	英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD
WOS记录号	WOS:000855295200015
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61022]
专题	中国科学院数学与系统科学研究院
通讯作者	Cheng, Daizhan
作者单位	1.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
推荐引用方式 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.