A switched system approach to the decidability of consensus.
Volume: 53 • Number: 5 • Pages: 3104-3119
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.