Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback

Christophe Zhang (1, 2)

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

We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized exponentially in that space and, for any given decay rate, we give an explicit feedback law that achieves that decay rate.

Mots clés: Internal control; Backstepping; Fredholm transformations; Transport equation; Rapid stabilization; transport equation

Domaines: Optimisation et contrôle [math.OC]

Christophe Zhang. Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback. 2020. ⟨hal-01905098v3⟩