Null controllability and finite-time stabilization in minimal time of one-dimensional first-order $2 \times 2$ linear hyperbolic systems

Long Hu (1) , Guillaume Olive (2)

1 School of Mathematics [Shandong]
2 Institute of Mathematics [Krakow]

The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order $2 \times 2$ linear hyperbolic systems. The main technical point is to show that we cannot obtain a better time. The proof combines the backstepping method with the Titchmarsh convolution theorem.

Mots clés: Hyperbolic systems; Boundary controllability; Minimal control time; Backstepping method; Titchmarsh convolution theorem

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

Long Hu, Guillaume Olive. Null controllability and finite-time stabilization in minimal time of one-dimensional first-order $2 \times 2$ linear hyperbolic systems. 2020. ⟨hal-02983321⟩