A bound for the rank-one transient of inhomogeneous matrix products in special case
Arthur Kennedy-Cochran-Patrick; Sergeĭ Sergeev; Štefan Berežný
Kybernetika (2019)
- Volume: 55, Issue: 1, page 12-23
- ISSN: 0023-5954
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topKennedy-Cochran-Patrick, Arthur, Sergeev, Sergeĭ, and Berežný, Štefan. "A bound for the rank-one transient of inhomogeneous matrix products in special case." Kybernetika 55.1 (2019): 12-23. <http://eudml.org/doc/294579>.
@article{Kennedy2019,
abstract = {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.},
author = {Kennedy-Cochran-Patrick, Arthur, Sergeev, Sergeĭ, Berežný, Štefan},
journal = {Kybernetika},
keywords = {max-plus algebra; matrix product; rank-one; walk; Trellis digraph},
language = {eng},
number = {1},
pages = {12-23},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A bound for the rank-one transient of inhomogeneous matrix products in special case},
url = {http://eudml.org/doc/294579},
volume = {55},
year = {2019},
}
TY - JOUR
AU - Kennedy-Cochran-Patrick, Arthur
AU - Sergeev, Sergeĭ
AU - Berežný, Štefan
TI - A bound for the rank-one transient of inhomogeneous matrix products in special case
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 1
SP - 12
EP - 23
AB - 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.
LA - eng
KW - max-plus algebra; matrix product; rank-one; walk; Trellis digraph
UR - http://eudml.org/doc/294579
ER -
References
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- Butkovic, P., 10.1007/978-1-84996-299-5, Springer Monographs in Mathematics, London 2010. MR2681232DOI10.1007/978-1-84996-299-5
- Kersbergen, B., Modeling and Control of Switching Max-Plus-Linear Systems., Ph.D. Thesis, TU Delft 2015.
- Merlet, G., Nowak, T., Sergeev, S., 10.1016/j.laa.2014.07.027, Linear Algebra Appl. 461 (2014), 163-199. MR3252607DOI10.1016/j.laa.2014.07.027
- Merlet, G., Nowak, T., Schneider, H., Sergeev, S., 10.1016/j.dam.2014.06.026, Discrete Appl. Math. 178 (2014), 121-134. MR3258169DOI10.1016/j.dam.2014.06.026
- Shue, L., Anderson, B. D. O., Dey, S., 10.1109/acc.1998.707354, In: Proc. American Control Conference, Philadelphia, Pensylvania 1998, pp. 1909-1913. DOI10.1109/acc.1998.707354
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