  This paper studies the informativity problem for reachability and
null-controllability of constrained systems. To be precise, we will focus on an
unknown linear systems with convex conic constraints from which we measure data
consisting of exact state trajectories of finite length. We are interested in
performing system analysis of such an unknown system on the basis of the
measured data. However, from such measurements it is only possible to obtain a
unique system explaining the data in very restrictive cases. This means that we
can not approach this problem using system identification combined with model
based analysis. As such, we will formulate conditions on the data under which
any such system consistent with the measurements is guaranteed to be reachable
or null-controllable. These conditions are stated in terms of spectral
conditions and subspace inclusions, and therefore they are easy to verify.
