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Rapid stabilization and observation of oscillating systems at different time instants

Abstract : This works contains two independent parts, each one dealing with the control of partial differential equations. In the first part, we study an explicit and already known feedback law that applies to linear, time-reversible systems, with a possibly unbounded control operator. We prove the well-posedness of the closed-loop problem in the semi-group framework and we study the decay rate of the solutions. In the second part, we give conditions on the choice of some time instants, such that the positions of a vibrating string (or beam) at these times enable to recover the initial data. The method relies on Diophantine approximation results. Using a duality method, we give a related exact controllability result.
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https://tel.archives-ouvertes.fr/tel-00864407
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Submitted on : Saturday, September 21, 2013 - 3:32:04 PM
Last modification on : Friday, June 19, 2020 - 9:22:04 AM
Long-term archiving on: : Sunday, December 22, 2013 - 3:00:18 AM

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  • HAL Id : tel-00864407, version 1

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Ambroise Vest. Rapid stabilization and observation of oscillating systems at different time instants. General Mathematics [math.GM]. Université de Strasbourg, 2013. English. ⟨NNT : 2013STRAD045⟩. ⟨tel-00864407⟩

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