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.

Revised:

Accepted:

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^{1}; Ferrante, Francesco

^{2}; Prieur, Christophe

^{3}

@article{CRMATH_2022__360_G3_219_0, author = {Dus, Mathias and Ferrante, Francesco and Prieur, Christophe}, 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}, number = {G3}, year = {2022}, doi = {10.5802/crmath.288}, language = {en}, url = {http://www.numdam.org/articles/10.5802/crmath.288/} }

TY - JOUR AU - Dus, Mathias AU - Ferrante, Francesco AU - Prieur, Christophe TI - Spectral stabilization of linear transport equations with boundary and in-domain couplings JO - Comptes Rendus. Mathématique PY - 2022 SP - 219 EP - 240 VL - 360 IS - G3 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.288/ DO - 10.5802/crmath.288 LA - en ID - CRMATH_2022__360_G3_219_0 ER -

%0 Journal Article %A Dus, Mathias %A Ferrante, Francesco %A Prieur, Christophe %T Spectral stabilization of linear transport equations with boundary and in-domain couplings %J Comptes Rendus. Mathématique %D 2022 %P 219-240 %V 360 %N G3 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.288/ %R 10.5802/crmath.288 %G en %F CRMATH_2022__360_G3_219_0

Dus, Mathias; Ferrante, Francesco; Prieur, Christophe. Spectral stabilization of linear transport equations with boundary and in-domain couplings. Comptes Rendus. Mathématique, Volume 360 (2022) no. G3, pp. 219-240. doi : 10.5802/crmath.288. http://www.numdam.org/articles/10.5802/crmath.288/

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