An Overview of Transience Bounds in Max-Plus Algebra

Thomas Nowak 1, * Bernadette Charron-Bost 2
* Corresponding author
1 DYOGENE - Dynamics of Geometric Networks
CNRS - Centre National de la Recherche Scientifique : UMR8548, Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : We survey and discuss upper bounds on the length of the transient phase of max-plus linear systems and sequences of max-plus matrix powers. In particular, we explain how to extend a result by Nachtigall to yield a new approach for proving such bounds and we state an asymptotic tightness result by using an example given by Hartmann and Arguelles.
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Thomas Nowak, Bernadette Charron-Bost. An Overview of Transience Bounds in Max-Plus Algebra. G. L. Litvinov; S. N. Sergeev. Tropical and Idempotent Mathematics and Applications, AMS, pp.277-289, 2014, Contemporary Mathematics, 978-0-8218-9496-5 (print); 978-1-4704-1684-3 (online). ⟨10.1090/conm/616/12306⟩. ⟨hal-00993630⟩

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