Closed-loop (CL) poles estimated from open-loop (OL) data can serve as useful features for system
interrogation and, in control applications, for checking discrepancies between the eigenstructure specified
during design, which reflects model properties, and the eigenstructure that would actually be realized in a
test. While estimating OL poles from OL data does not depend on assumption made on the inter-sample
behavior of the inputs, this is not the case for CL poles because these are affected by how the non-homogeneous part of the discrete-time model is mapped to continuous time. Analysis shows that errors arising from treating typically band-limited OL inputs as zero-order hold (an assumption often adopted by
default) can be significant, even at sampling rates frequently considered high enough to ignore inter-sample
concerns. Also shown is the fact that the straightforward approach of closing the loop on a modally
truncated state-space realization does not yield the poles of the truncated CL system and that analytical
consistency requires that the feedback be accounted for at the level of the experimentally estimated transfer
matrices. Finally, it is shown that pole extraction from experimental transfer matrices can be decoupled
from the residues by adopting a fitness function based on subspace angles (instead of transfer matrix misfit
norms) and that this leads to increases in the basin of attraction of the global minimum.
20 May 2026