A switched system approach to the decidability of consensus.

Chevalier, Pierre-Yves;Hendrickx, Julien;Jungers, Raphaël
(2015) SIAM Journal on Control and Optimization — Vol. 53, n° 5, p. 3104-3119 (2015)

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Abstract— The convergence to consensus of all products of a given set of matrices is known to be algorithmically decidable when all matrices in the set are stochastic. We formulate this question as a stability problem for switched systems, and show that the decidability result remains valid for more general classes than stochastic matrices. Our results make use of a general theorem of Lagarias and Wang on the convergence of switched systems, and allow showing as a byproduct that the bound provided by this theorem is tight.
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Chevalier, P.-Y., Hendrickx, J., & Jungers, R. (2015). A switched system approach to the decidability of consensus. SIAM Journal on Control and Optimization, 53(5), 3104-3119. https://hdl.handle.net/2078.5/53579 (Original work published 2015)