  In this paper we investigate a data-driven approach to the design of an
unknown-input observer (UIO). Specifically, we provide necessary and sufficient
conditions for the existence of an unknown-input observer for a discrete-time
linear time-invariant (LTI) system, designed based only on some available data,
obtained on a finite time window. We also prove that, under weak assumptions on
the collected data, the solvability conditions derived by means of the
data-driven approach are in fact equivalent to those obtained through the
model-based one. In other words, the data-driven conditions do not impose
further constraints with respect to the classic model-based ones, expressed in
terms of the original system matrices.
