| 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:
|
http://hdl.handle.net/10338.dmlcz/147703 |
| . |
| 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 |
| . |
