@article{Taha2026a,
abstract = {This letter revisits the classical PBH test through the lens of finite-horizon reachability. By casting state transfer as a minimum energy, primal optimization problem, we show that unreachable state-space maneuvers admit dual infeasibility certificates. These certificates are computable without forming the controllability matrix meaning that uncontrollability can be efficiently certified. We prove that any such certificate is a linear combination of uncontrollable generalized eigenvectors, thereby providing a spectral interpretation without a global eigendecomposition. We also devise algorithms based on Krylov sub-space methods that extract some of the uncontrollable PBH modes from a certificate and demonstrate favorable scaling on large dynamic networks with thousands of nodes.},
archivePrefix = {arXiv},
arxivId = {2606.15181},
author = {Taha, Ahmad F. and Kazma, Mohamad H. and Albustami, Abdallah A.},
doi = {10.1109/LCSYS.2026.3700807},
eprint = {2606.15181},
journal = {IEEE Control Systems Letters},
title = {{Revisiting the PBH Test: Fast Uncontrollability Certificates via Krylov Methods}},
url = {https://doi.org/10.1109/LCSYS.2026.3700807},
year = {2026}
}