Article
MSC:
05C20,
05C22,
05C25,
15A80,
16Y60,
68R99 | MR 3935412 | Zbl 07088876 | DOI: 10.14736/kyb-2019-1-0012
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
max-plus algebra; matrix product; rank-one; walk; Trellis digraph
max-plus algebra; matrix product; rank-one; walk; Trellis digraph
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.
References:
[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
[2] Butkovic, P.: Max-linear Systems: Theory and Algorithms. Springer Monographs in Mathematics, London 2010. DOI 10.1007/978-1-84996-299-5 | MR 2681232
[3] Kersbergen, B.: Modeling and Control of Switching Max-Plus-Linear Systems. Ph.D. Thesis, TU Delft 2015.
[4] Merlet, G., Nowak, T., Sergeev, S.: Weak CSR expansions and transience bounds in max-plus algebra. Linear Algebra Appl. 461 (2014), 163-199. DOI 10.1016/j.laa.2014.07.027 | MR 3252607
[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. DOI 10.1016/j.dam.2014.06.026 | MR 3258169
[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. DOI 10.1109/acc.1998.707354
Search
Partner of
