  We provide out-of-sample certificates on the controlled invariance property
of a given set with respect to a class of black-box linear systems.
Specifically, we consider linear time-invariant models whose state space
matrices are known only to belong to a certain family due to a possibly inexact
quantification of some parameters. By exploiting a set of realizations of those
undetermined parameters, verifying the controlled invariance property of the
given set amounts to a linear program, whose feasibility allows us to establish
an a-posteriori probabilistic certificate on the controlled invariance property
of such a set with respect to the nominal linear time-invariant dynamics. The
proposed framework is applied to the control of a networked multi-agent system
with unknown weighted graph.
