Geodesic
An upper bound of the reachability index for a special class of positive 2-D systems
The electronic journal of linear algebra, Tome 18 (2009), pp. 1-12.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The smallest number of steps needed to reach all nonnegative local states of a positive two-dimensional (2-D) system is the local reachability index of the system. The study of such a number is still an open problem which seems to be a hard task. In this paper, an expression depending on the dimension n as well as an upper bound on the local reachability index of a special class of systems are derived. Moreover, this reachability index is greater than any other bound proposed in previous literature.
Classification : 93C55, 15A48, 93B03
Keywords: Hurwitz products, influence digraph, local reachability index, nonnegative matrices, positive two-dimensional (2-D) systems, reachability 
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     title = {An upper bound of the reachability index for a special class of positive {2-D} systems},
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Bailo, Esteban; Gelonch, Josep; Romero-Vivo, Sergio. An upper bound of the reachability index for a special class of positive 2-D systems. The electronic journal of linear algebra, Tome 18 (2009), pp. 1-12. http://geodesic.mathdoc.fr/item/ELA_2009__18__a57/