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

On Barriers in State and Input Constrained Nonlinear Systems