On the Equivalence of Model-Based and Data-Driven Approaches to the Design of Unknown-Input Observers

In this article, 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 a UIO for a discrete-time linear time-invariant 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.