Comptes Rendus
Théorie du contrôle
Spectral stabilization of linear transport equations with boundary and in-domain couplings
Mathias Dus1 ; Francesco Ferrante2 ; Christophe Prieur3
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.

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.

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DOI : 10.5802/crmath.288
Classification : 93D05, 93D15, 93D20
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 
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     title = {Spectral stabilization of linear transport equations with boundary and in-domain couplings},
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     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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