  This paper is devoted to the controllability of a general linear hyperbolic
system in one space dimension using boundary controls on one side. Under
precise and generic assumptions on the boundary conditions on the other side,
we previously established the optimal time for the null and the exact
controllability for this system for a generic source term. In this work, we
prove the null-controllability for any time greater than the optimal time and
for any source term. Similar results for the exact controllability are also
discussed.
