[Spectral compensation and optimal energy decay rate for partially damped systems]
We study the stabilization of systems of two equations, for which only one equation is damped by a feedback control. We show that a well chosen control can compensate the real parts of the eigenvalues of the system, therefore, giving the optimal polynomial energy decay rate of the system for smooth initial data.
Nous étudions la stabilisation d'un système de deux équations linéaires, dont une seule équation est amortie par un contrôle feedback. Nous montrons qu'un contrôle convenablement choisi peut compenser les parties réelles des valeures propres du système, et donc fournir le meilleur taux de décroissance polynomiale de l'énergie du système pour des données initiales régulières.
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@article{CRMATH_2003__337_8_531_0,
author = {Loreti, Paola and Rao, Bopeng},
title = {Compensation spectrale et taux de d\'ecroissance optimal de~l'\'energie de syst\`emes partiellement amortis},
journal = {Comptes Rendus. Math\'ematique},
pages = {531--536},
publisher = {Elsevier},
volume = {337},
number = {8},
year = {2003},
doi = {10.1016/j.crma.2003.08.009},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2003.08.009/}
}
TY - JOUR AU - Loreti, Paola AU - Rao, Bopeng TI - Compensation spectrale et taux de décroissance optimal de l'énergie de systèmes partiellement amortis JO - Comptes Rendus. Mathématique PY - 2003 SP - 531 EP - 536 VL - 337 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2003.08.009/ DO - 10.1016/j.crma.2003.08.009 LA - fr ID - CRMATH_2003__337_8_531_0 ER -
%0 Journal Article %A Loreti, Paola %A Rao, Bopeng %T Compensation spectrale et taux de décroissance optimal de l'énergie de systèmes partiellement amortis %J Comptes Rendus. Mathématique %D 2003 %P 531-536 %V 337 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2003.08.009/ %R 10.1016/j.crma.2003.08.009 %G fr %F CRMATH_2003__337_8_531_0
Loreti, Paola; Rao, Bopeng. Compensation spectrale et taux de décroissance optimal de l'énergie de systèmes partiellement amortis. Comptes Rendus. Mathématique, Volume 337 (2003) no. 8, pp. 531-536. doi : 10.1016/j.crma.2003.08.009. http://www.numdam.org/articles/10.1016/j.crma.2003.08.009/
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