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Title: A bound for the rank-one transient of inhomogeneous matrix products in special case (English)
Author: Kennedy-Cochran-Patrick, Arthur
Author: Sergeev, Sergeĭ
Author: Berežný, Štefan
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 55
Issue: 1
Year: 2019
Pages: 12-23
Summary lang: English
Category: math
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 [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one. (English)
Keyword: max-plus algebra
Keyword: matrix product
Keyword: rank-one
Keyword: walk
Keyword: Trellis digraph
MSC: 05C20
MSC: 05C22
MSC: 05C25
MSC: 15A80
MSC: 16Y60
MSC: 68R99
idZBL: Zbl 07088876
idMR: MR3935412
DOI: 10.14736/kyb-2019-1-0012
Date available: 2019-05-07T11:02:09Z
Last updated: 2020-02-27
Stable URL:
Reference: [1] Baccelli, F. L., Cohen, G., Olsder, G. J., Quadrat, J. P.: Synchronization and Linearity: An Algebra for Discrete Event Systems..John Wiley and Sons, Hoboken 1992. MR 1204266
Reference: [2] Butkovic, P.: Max-linear Systems: Theory and Algorithms..Springer Monographs in Mathematics, London 2010. MR 2681232, 10.1007/978-1-84996-299-5
Reference: [3] Kersbergen, B.: Modeling and Control of Switching Max-Plus-Linear Systems..Ph.D. Thesis, TU Delft 2015.
Reference: [4] Merlet, G., Nowak, T., Sergeev, S.: Weak CSR expansions and transience bounds in max-plus algebra..Linear Algebra Appl. 461 (2014), 163-199. MR 3252607, 10.1016/j.laa.2014.07.027
Reference: [5] Merlet, G., Nowak, T., Schneider, H., Sergeev, S.: Generalizations of bounds on the index of convergence to weighted digraphs..Discrete Appl. Math. 178 (2014), 121-134. MR 3258169, 10.1016/j.dam.2014.06.026
Reference: [6] Shue, L., Anderson, B. D. O., Dey, S.: On steady state properties of certain max-plus products..In: Proc. American Control Conference, Philadelphia, Pensylvania 1998, pp. 1909-1913. 10.1109/acc.1998.707354


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