Equivalent one-dimensional first-order linear hyperbolic systems and range of the minimal null control time with respect to the internal coupling matrix

Long Hu (1) , Guillaume Olive (2)

1 Shandong University
2 Faculty of Mathematics and Computer Science of the Jagiellonian University

In this paper, we are interested in the minimal null control time of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls. Our main result is an explicit characterization of the smallest and largest values that this minimal null control time can take with respect to the internal coupling matrix. In particular, we obtain a complete description of the situations where the minimal null control time is invariant with respect to all the possible choices of internal coupling matrices. The proof relies on the notion of equivalent systems, in particular the backstepping method, a canonical $LU$-decomposition for boundary coupling matrices and a compactness-uniqueness method adapted to the null controllability property.

Mots clés: Hyperbolic systems; Boundary controllability; Minimal null control time; Equivalent systems; Backstepping method; LU-decomposition; Compactness-uniqueness method

Domaines: Optimisation et contrôle [math.OC]

Long Hu, Guillaume Olive. Equivalent one-dimensional first-order linear hyperbolic systems and range of the minimal null control time with respect to the internal coupling matrix. Journal of Differential Equations, 2022, 336, pp.654-707. ⟨10.1016/j.jde.2022.07.023⟩. ⟨hal-03346287v2⟩