  In this paper, we propose an extension to mixed multidimensional constraints
of the problem of state and input constrained control introduced in DeDona and
L\'evine, SIAM J. Control and Optimiz., Vol. 51, 2013, where the admissible
set, namely the subset of the state space where the state and input constraints
can be satisfied for all times, was studied, with focus on its boundary. The
latter may be divided in two parts, one of them being called barrier, a
semipermeable surface. We extend this notion of barrier to the mixed case and
prove that it can be constructed via a minimum-like principle involving the
Karush-K\"uhn-Tucker multipliers associated to the constraints and a
generalised gradient condition at its endpoints.
