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Stabilizability of Infinite-Dimensional Systems by Finite-Dimensional Controls

Jean-Pierre Raymond
This article has been retracted. Retraction note.

Abstract

In this paper, we consider control systems for which the underlying semigroup is analytic, and the resolvent of its generator is compact. In that case we give a characterization of the stabilizability of such control systems. When the stabilizability condition is satisfied the system is also stabilizable by finite-dimensional controls. We end the paper by giving an application of this result to the stabilizability of the Oseen equations with mixed boundary conditions.

Funding source: Agence Nationale de la Recherche

Award Identifier / Grant number: ANR 15-CE40.0010

Funding statement: The author is partially supported by the ANR-Project IFSMACS (ANR 15-CE40.0010).

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Received: 2017-12-02
Revised: 2018-05-31
Accepted: 2018-06-10
Published Online: 2018-07-07
Published in Print: 2019-10-01

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