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Zbl 1157.93514
Cao, Ming; Morse, A.Stephen; Anderson, Brian D.O.
Reaching a consensus in a dynamically changing environment: a graphical approach. (English)
[J] SIAM J. Control Optim. 47, No. 2, 575-600 (2008). ISSN 0363-0129; ISSN 1095-7138/e

Summary: This paper presents new graph-theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments. The concepts of rooted, strongly rooted, and neighbor-shared are defined, and conditions are derived for compositions of sequences of directed graphs to be of these types. The graph of a stochastic matrix is defined, and it is shown that under certain conditions the graph of a Sarymsakov matrix and a rooted graph are one and the same. As an illustration of the use of the concepts developed in this paper, graph-theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied Vicsek consensus problem.

MSC 2000:: *93E03 General theory of stochastic systems
05C50 Graphs and matrices
05C75 Structural characterization of types of graphs
15A51 Stochastic matrices
40A20 Convergence of infinite products
68W15 Distributed algorithms
93C85 Automated control systems

Keywords: cooperative control; graph theory; switched systems; multiagent systems

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