Minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls

In this article we study the minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems when all the controls are acting on the same side of the boundary. We establish an explicit and easy-to-compute formula for this time with respect to all the coupling parameters of the system. This partially solves an open problem raised in the celebrated survey [Rus78] and in the article [Hu15]. The proof relies on the introduction of a canonical $UL$-decomposition and the compactness-uniqueness method.