Data-Driven Reduced-Order Unknown-Input Observers

The paper’s Theorem 9 characterizes data-driven rUIO existence via the linear relation Xf,1 = [S1 S2 S3 S4][Up; Yp; Yf; Xp,1] with S4 Schur and provides the parameterization AUIO=S4, Bu_UIO=S1, By_UIO=S2+S4S3, DUIO=S3; this is precisely what the candidate solution proves, matching Proposition 6 and Theorem 9. The candidate’s necessity and construction align exactly with the paper’s mapping. The only gap is a proof step that invokes a full-row-rank assumption on a stacked matrix including the unmeasured disturbance; the paper instead correctly bases sufficiency on the kernel-inclusion/compatibility condition, avoiding dependence on unknown d. With that minor fix, the candidate’s proof lines up with the paper’s results and intent (Definition 1, Proposition 6, Theorem 9).