  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.
