On the structural properties of an efficient feedback law

Ambroise Vest

doi:10.3934/eect.2013.2.543

Article Contents

2013, Volume 2, Issue 3: 543-556. Doi: 10.3934/eect.2013.2.543

This issue Previous Article Energy methods for Hartree type equations with inverse-square potentials Next Article

On the structural properties of an efficient feedback law

Ambroise Vest^1,

1.
Institut de Recherche Mathématique Avancée, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg Cédex

Received: January 31, 2013

Revised: April 30, 2013

Published: August 2013

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Abstract

We investigate some structural properties of an efficient feedback law that stabilize linear time-reversible systems with an arbitrarily large decay rate. After giving a short proof of the generation of a group by the closed-loop operator, we focus on the domain of the infinitesimal generator in order to illustrate the difference between a distributed control and a boundary control, the latter being technically more complex. We also give a new proof of the exponential decay of the solutions and we provide an explanation of the higher decay rate observed in some experiments.

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Mathematics Subject Classification: Primary: 93D15; Secondary: 93C05, 47D06, 93C20.

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