Geodesic
A bound for the rank-one transient of inhomogeneous matrix products in special case
Kybernetika, Tome 55 (2019) no. 1, pp. 12-23
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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.
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.
DOI : 10.14736/kyb-2019-1-0012
Classification : 05C20, 05C22, 05C25, 15A80, 16Y60, 68R99
Keywords: max-plus algebra; matrix product; rank-one; walk; Trellis digraph 
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Kennedy-Cochran-Patrick, Arthur; Sergeev, Sergeĭ; Berežný, Štefan. A bound for the rank-one transient of inhomogeneous matrix products in special case. Kybernetika, Tome 55 (2019) no. 1, pp. 12-23. doi: 10.14736/kyb-2019-1-0012

[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

[2] Butkovic, P.: Max-linear Systems: Theory and Algorithms. Springer Monographs in Mathematics, London 2010. | DOI | MR

[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 | MR

[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 | MR

[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

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