Distributed Bounds on the Algebraic Connectivity of Graphs With Application to Agent Networks

doi:10.1109/TCYB.2016.2601961

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	Distributed Bounds on the Algebraic Connectivity of Graphs With Application to Agent Networks
	Li, Xiuxian 1; Chen, Michael Z. Q.1; Su, Housheng 2; Li, Chanying3
刊名	IEEE TRANSACTIONS ON CYBERNETICS
	2017-08-01
卷号	47 期号:8 页码:2121-2131
关键词	Agent networks distributed bounds spectral radius the algebraic connectivity the Laplacian matrix
ISSN号	2168-2267
DOI	10.1109/TCYB.2016.2601961
英文摘要	This paper establishes several bounds on the algebraic connectivity and spectral radius of graphs. Before deriving these bounds, a directed graph with a leader node is first investigated, for which some bounds on the spectral radius and the smallest real part of all the eigenvalues of M = L + D are obtained using the properties of M-matrix and non-negative matrix under a mild assumption, where L is the Laplacian matrix of the graph and D = diag{d(1), d(2),..., d(N)} with d(i) > 0 if node i can access the information of the leader node and 0 otherwise. Subsequently, by virtue of the results on directed graphs, the bounds on the algebraic connectivity and spectral radius of an undirected connected graph are provided. Besides establishing these bounds, another important feature is that all these bounds are distributed in the sense of only knowing the information of edge weights' bounds and the number of nodes in a graph, without using any information of inherent structures of the graph. Therefore, these bounds can be in some sense applied to agent networks for reducing the conservatism where control gains in control protocols depend on the eigenvalues of matrices M or L, which are global information. Also some examples are provided for corroborating the feasibility of the theoretical results.
资助项目	National Natural Science Foundation of China[61374053] ; National Natural Science Foundation of China[61473129] ; National Natural Science Foundation of China[61422308] ; General Research Fund[17205414] ; Program for New Century Excellent Talents in University from Chinese Ministry of Education[NCET-12-0215]
WOS研究方向	Computer Science
语种	英语
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
WOS记录号	WOS:000405458200029
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/25927]
专题	系统科学研究所
通讯作者	Chen, Michael Z. Q.
作者单位	1.Univ Hong Kong, Dept Mech Engn, Hong Kong, Hong Kong, Peoples R China 2.Huazhong Univ Sci & Technol, Sch Automat, Image Proc & Intelligent Control Key Lab, Educ Minist China, Wuhan 430074, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Xiuxian,Chen, Michael Z. Q.,Su, Housheng,et al. Distributed Bounds on the Algebraic Connectivity of Graphs With Application to Agent Networks[J]. IEEE TRANSACTIONS ON CYBERNETICS,2017,47(8):2121-2131.
APA	Li, Xiuxian,Chen, Michael Z. Q.,Su, Housheng,&Li, Chanying.(2017).Distributed Bounds on the Algebraic Connectivity of Graphs With Application to Agent Networks.IEEE TRANSACTIONS ON CYBERNETICS,47(8),2121-2131.
MLA	Li, Xiuxian,et al."Distributed Bounds on the Algebraic Connectivity of Graphs With Application to Agent Networks".IEEE TRANSACTIONS ON CYBERNETICS 47.8(2017):2121-2131.