Hypocoercivity and hypocontractivity concepts for linear dynamical systems

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Franz Achleitner
https://orcid.org/0000-0002-9306-880X
Anton Arnold
https://orcid.org/0000-0001-9923-2888
Volker Mehrmann
https://orcid.org/0000-0001-5051-2870

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.

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