[Observabilité polynomiale uniforme des systèmes linéaires conservatifs semi-discrets en temps]
Dans cet article nous étudions la semi-discrétisation en temps des systèmes de dimension infinie qui sont polynomialement observables. En utilisant une méthode basée sur l’estimation de la résolvante, nous obtenons des inégalités d’observabilité polynomiale uniformes pour les solutions filtrées du problème semi-discret en temps. Nous présentons également des applications de notre résultat aux problèmes de stabilisation.
In this paper we study time semi-discrete approximations of a class of polynomially observable infinite dimensional systems. By using a method based on the resolvent estimate, we derive uniform polynomial observability inequalities within a class of solutions of the time-discrete problem in which the high frequency components have been filtered. We also present an application of our result to stabilization problems.
Mots clés : Observability inequality, Time discretization, Filtering
@article{AMBP_2016__23_1_53_0,
author = {Hajjej, Zayd},
title = {Uniform polynomial observability of time-discrete conservative linear systems},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {53--73},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {23},
number = {1},
year = {2016},
doi = {10.5802/ambp.354},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.354/}
}
TY - JOUR AU - Hajjej, Zayd TI - Uniform polynomial observability of time-discrete conservative linear systems JO - Annales mathématiques Blaise Pascal PY - 2016 SP - 53 EP - 73 VL - 23 IS - 1 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.354/ DO - 10.5802/ambp.354 LA - en ID - AMBP_2016__23_1_53_0 ER -
%0 Journal Article %A Hajjej, Zayd %T Uniform polynomial observability of time-discrete conservative linear systems %J Annales mathématiques Blaise Pascal %D 2016 %P 53-73 %V 23 %N 1 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.354/ %R 10.5802/ambp.354 %G en %F AMBP_2016__23_1_53_0
Hajjej, Zayd. Uniform polynomial observability of time-discrete conservative linear systems. Annales mathématiques Blaise Pascal, Tome 23 (2016) no. 1, pp. 53-73. doi : 10.5802/ambp.354. http://www.numdam.org/articles/10.5802/ambp.354/
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