Data-Driven Meets Geometric Control: Zero Dynamics, Subspace Stabilization, and Malicious Attacks

Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the invariant subspaces of interest. In this letter we overcome this limitation by finding direct data-driven formulas for some of the foundational tools of the geometric approach. We use our results to (i) find a feedback gain that confines the system state within a subspace, (ii) compute the invariant zeros of the unknown system, and (iii) design attacks that remain undetectable.