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}
}

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