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Title: Convergence of infinite products of stochastic matrices : a graphical decomposition criterion
Authors: Chen, Y
Xiong, W
Li, F
Keywords: Graphical decomposition
Infinite products of stochastic matrices
Issue Date: 2016
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on automatic control, 2016, v. 61, no. 11, 7393494, p. 3599-3605 How to cite?
Journal: IEEE transactions on automatic control 
Abstract: This technical note presents a convergence criterion for infinite products of stochastic matrices which is based on graphical decomposition of the associated graphs. We show that if the associated graphs of a set of stochastic matrices share a common graphical decomposition and the corresponding reduced graphs are rooted, then any infinite products of the given set of stochastic matrices is convergent. Specifically, we propose a numerical algorithm for finding the common graphical decomposition of the associated graphs, which has been proved to be polynomial-time fast. The proposed criterion can be applied directly to a series of classical results in distributed coordination algorithm.
ISSN: 0018-9286
EISSN: 1558-2523
DOI: 10.1109/TAC.2016.2521782
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