  In this paper, the problem of state and input constrained control is
addressed, with multidimensional constraints. We obtain a local description of
the boundary of the admissible subset of the state space where the state and
input constraints can be satisfied \emph{for all times}. This boundary is made
of two disjoint parts: the subset of the state constraint boundary on which
there are trajectories pointing towards the interior of the admissible set or
tangentially to it; and a barrier, namely a semipermeable surface which is
constructed via a minimum-like principle.
