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Infinite-time admissibility under compact perturbations

: Schmid, J.


Kerner, J.:
Control Theory of Infinite-Dimensional Systems : Workshop on "Control theory of infinite-dimensional systems", January 10-12, 2018, Hagen
Cham: Springer Nature, 2020 (Operator theory. Advances and applications 277)
ISBN: 978-3-030-35897-6 (Print)
ISBN: 978-3-030-35898-3 (Online)
Workshop on "Control theory of Infinite-Dimensional Systems" <2018, Hagen>
Conference Paper
Fraunhofer ITWM ()

We investigate the behavior of infinite-time admissibility under compact perturbations. We show, by means of two completely different examples, that infinite-time admissibility is not preserved under compact perturbations Q of the underlying semigroup generator A, even if A and A + Q both generate strongly stable semigroups.