Applications of Laplace-Carleson embeddings to admissibility and controllability

TL;DR

This paper explores how Laplace-Carleson embedding results can be used to improve understanding of admissibility and controllability in linear semigroup systems, introducing new theoretical results and characterizations.

Contribution

It introduces new Laplace-Carleson embedding results and applies them to establish broader criteria for admissibility and controllability in linear systems.

Findings

New Carleson embedding theorem for analytic semigroups

Extended criteria for weighted admissibility of control and observation operators

Characterization of controllability by smoother inputs via weighted interpolation

Abstract

It is shown how results on Carleson embeddings induced by the Laplace transform can be use to derive new and more general results concerning the weighted admissibility of control and observation operators for linear semigroup systems with q-Riesz bases of eigenvectors. Next, a new Carleson embedding result is proved, which gives further results on weighted admissibility for analytic semigroups. Finally, controllability by smoother inputs is characterised by means of a new result about weighted interpolation.