Reaching a Consensus in a Dynamically Changing Environment: A Graphical Approach

Authors:
Ming Cao;A. Stephen Morse;Brian D. O. Anderson
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2008

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Abstract

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.