Hypocoercivity and hypocontractivity concepts for linear dynamical systems
Dynamical Systems
2023-08-21 v3
Abstract
For linear dynamical systems (in continuous-time and discrete-time) we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the relations of these concepts to (asymptotic) stability, as well as (semi-)dissipativity and (semi-)contractivity, respectively. On the basis of these results, the short-time behavior of the propagator norm for linear continuous-time and discrete-time systems is characterized by the (shifted) hypocoercivity index and the (scaled) hypocontractivity index, respectively.
Cite
@article{arxiv.2204.13033,
title = {Hypocoercivity and hypocontractivity concepts for linear dynamical systems},
author = {Franz Achleitner and Anton Arnold and Volker Mehrmann},
journal= {arXiv preprint arXiv:2204.13033},
year = {2023}
}
Comments
29 pages, 3 figures, 2 tables