  For a discrete-time linear system, we use data from a single open-loop
experiment to design directly a feedback controller enforcing that a given
(polyhedral) set of the state is invariant and given (polyhedral) constraints
on the control are satisfied. By building on classical results from model-based
set invariance and a fundamental result from Willems et al., the controller
designed from data has the following desirable features. The satisfaction of
the above properties is guaranteed only from data, it can be assessed by
solving a numerically-efficient linear program, and, under a certain rank
condition, a data-based solution is feasible if and only if a model-based
solution is feasible.
