Hypocoercivity and hypocontractivity concepts for linear dynamical systems
Authors
Franz Achleitner, Anton Arnold, Volker Mehrmann
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.
Citation
- Journal: The Electronic Journal of Linear Algebra
- Year: 2023
- Volume: 39
- Issue:
- Pages: 33–61
- Publisher: University of Wyoming Libraries
- DOI: 10.13001/ela.2023.7531
BibTeX
@article{Achleitner_2023,
title={{Hypocoercivity and hypocontractivity concepts for linear dynamical systems}},
volume={39},
ISSN={1081-3810},
DOI={10.13001/ela.2023.7531},
journal={The Electronic Journal of Linear Algebra},
publisher={University of Wyoming Libraries},
author={Achleitner, Franz and Arnold, Anton and Mehrmann, Volker},
year={2023},
pages={33--61}
}