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A bound for the rank-one transient of inhomogeneous matrix products in special case. (English) Zbl 1449.15064
Summary: We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [L. Shue, B. D. O. Anderson, and S. Dey, “On steady-state properties of certain max-plus products”, in: Proceedings of the 1998 American Control Conference, Philadelphia, Pensylvania, June 24-26,1998. Piscataway, NJ: IEEE. 1909–1913 (1998; doi:10.1109/acc.1998.707354]. We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.
MSC:
15A80 Max-plus and related algebras
16Y60 Semirings
05C20 Directed graphs (digraphs), tournaments
05C22 Signed and weighted graphs
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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References:
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