Finite-time internal stabilization of a linear 1-D transport equation

Christophe Zhang (1, 2)

1 CaGE - Control And GEometry
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We consider a 1-D linear transport equation on the interval (0, L), with an internal scalar control. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized in finite time, and we give an explicit feedback law.

Mots clés: Transport equation; Internal control; Backstepping; Finite-time; Fredholm transformations; Feedback stabilization

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Christophe Zhang. Finite-time internal stabilization of a linear 1-D transport equation. Systems and Control Letters, 2019, 133. ⟨hal-01980349v2⟩