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

Dus, Mathias; Ferrante, Francesco; Prieur, Christophe

Comptes Rendus. Mathématique, Tome 360 (2022) no. G3, 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.

Classification : 93D05, 93D15, 93D20

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