  This paper deals with developing tests for checking whether an unknown system
has certain structural properties. The tests that we are aiming at are in terms
of noisy input-state-output data obtained from the unknown system. Since, in
general, the data do not determine the unknown system uniquely, many systems
are compatible with the same set of data. Therefore we can not apply system
identification and apply existing, model based, tests. Instead, we will use the
concept of informativity, and establish tests for informativity of the given
noisy data. We will do this for a range of system properties, among which
strong observability and detectability and strong controllability and
stabilizability. These informativity tests will be in terms of rank tests on
polynomial matrices that can be constructed from the noisy data. We will also
set up a geometric framework for informativity analysis. Within that framework
we will give geometric tests for informativity for strong observability,
observability, and left-invertibilty.
