# Coupling Time of a (Max,Plus) Matrix

1 TRIO - Real time and interoperability
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In this note, we give a bound on the coupling time of an irreducible (max,plus) linear system $X(n) = A \otimes X(n-1)$ with its pseudo-periodic regime. This bounds uses a decomposition of the matrix $A$ into its critical part $A_c$ and its non-critical part $B$, as well as the maximal average weight of a circuit in $B$, which could be seen as the counterpart of the second largest eigenvalue in the classical linear case.
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https://hal.inria.fr/inria-00072568
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 10:18:17 AM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:13:31 PM

### Identifiers

• HAL Id : inria-00072568, version 1

### Citation

Anne Bouillard, Bruno Gaujal. Coupling Time of a (Max,Plus) Matrix. [Research Report] RR-4068, INRIA. 2000. ⟨inria-00072568⟩

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