  For an unknown linear system, starting from noisy open-loop input-state data
collected during a finite-length experiment, we directly design a linear
feedback controller that guarantees robust invariance of a given polyhedral set
of the state in the presence of disturbances. The main result is a necessary
and sufficient condition for the existence of such a controller, and amounts to
the solution of a linear program. The benefits of large and rich data sets for
the solution of the problem are discussed. A numerical example about a
simplified platoon of two vehicles illustrates the method.
