  The paper introduces a novel algorithm for computing the output admissible
set of linear discrete-time systems subject to input saturation. The proposed
method takes advantage of the piecewise-affine dynamics to propagate the output
constraints within the non-saturated and saturated regions. The constraints are
then shared between regions to ensure a proper transition from one region to
another. The resulting algorithm generates a set that is proven to be
polyhedral, safe, positively invariant, and finitely determined. Moreover, the
set is also proven to be strictly larger than the maximal output admissible set
that would be obtained by treating input saturation as a constraint.
