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arXiv · 2204.13033

Hypocoercivity and hypocontractivity concepts for linear dynamical systems

Franz Achleitner·Anton Arnold·Volker Mehrmann
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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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Franz Achleitner, Anton Arnold, Volker Mehrmann. 2022-04-27. Hypocoercivity and hypocontractivity concepts for linear dynamical systems. https://doi.org/10.13001/ela.2023.7531

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