Uniform polynomial observability of time-discrete conservative linear systems
[Observabilité polynomiale uniforme des systèmes linéaires conservatifs semi-discrets en temps]
Annales Mathématiques Blaise Pascal, Tome 23 (2016) no. 1, pp. 53-73.

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.

Publié le :
DOI : https://doi.org/10.5802/ambp.354
Classification : 93B07,  93C55,  65M06
Mots clés : Observability inequality, Time discretization, Filtering
@article{AMBP_2016__23_1_53_0,
     author = {Zayd Hajjej},
     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 = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.354/}
}
Zayd Hajjej. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.354/

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