Spectral stabilization of linear transport equations with boundary and in-domain couplings

Mathias Dus; Francesco Ferrante; Christophe Prieur

doi:10.5802/crmath.288

Théorie du contrôle

Spectral stabilization of linear transport equations with boundary and in-domain couplings

Mathias Dus ¹ ; Francesco Ferrante ² ; Christophe Prieur ³

¹ IMT Toulouse, 118 Route de Narbonne, 31400 Toulouse, France
² Department of Engineering, University of Perugia, Via G. Duranti, 67, 06125 Perugia, Italy
³ Univ. Grenoble Alpes, CNRS, Grenoble-INP, GIPSA-lab, 38000, Grenoble, France

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 219-240.

Résumé

In this work, the problem of stabilization of general systems of linear transport equations with in-domain and boundary couplings is investigated. It is proved that the unstable part of the spectrum is of finite cardinal. Then, using the pole placement theorem, a linear full state feedback controller is synthesized to stabilize the unstable finite-dimensional part of the system. Finally, by a careful study of semigroups, we prove the exponential stability of the closed-loop system. As a by product, the linear control constructed before is saturated and a fine estimate of the basin of attraction is given.

Reçu le : 2021-03-23
Révisé le : 2021-09-07
Accepté le : 2021-10-22
Publié le : 2022-03-31

DOI : 10.5802/crmath.288

Classification : 93D05, 93D15, 93D20

Affiliations des auteurs :

Mathias Dus ¹ ; Francesco Ferrante ² ; Christophe Prieur ³

¹ IMT Toulouse, 118 Route de Narbonne, 31400 Toulouse, France
² Department of Engineering, University of Perugia, Via G. Duranti, 67, 06125 Perugia, Italy
³ Univ. Grenoble Alpes, CNRS, Grenoble-INP, GIPSA-lab, 38000, Grenoble, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMATH_2022__360_G3_219_0,
     author = {Mathias Dus and Francesco Ferrante and Christophe Prieur},
     title = {Spectral stabilization of linear transport equations with boundary and in-domain couplings},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {219--240},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.288},
     language = {en},
}

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Mathias Dus; Francesco Ferrante; Christophe Prieur. Spectral stabilization of linear transport equations with boundary and in-domain couplings. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 219-240. doi : 10.5802/crmath.288. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.288/

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