bibkey: oymakozay2019lti authors: Samet Oymak; Necmiye Ozay year: 2019 title: Non-asymptotic Identification of LTI Systems from a Single Trajectory doi: null url: https://arxiv.org/abs/1806.05722v2 claim: Exact block-Hankel factorization and Ho-Kalman realization separate algebraic state dimension from statistical identification under additional input, noise and conditioning hypotheses. strata_touched: [] license: citation-only triage: anchor
Exact realization as an intermediate input
The primary text is arXiv:1806.05722v2. Section 2, p. 2, specifies real discrete state-space matrices and its zero-initial-state observation model. Section 5.1, pp. 7–8, uses the observability/controllability factorization and Ho-Kalman construction. Section 5.2, Theorem 5.3 and Corollary 5.4, p. 9, adds perturbation and singular-value conditions. Exact minimal realization requires sufficient block horizons and the reachable/observable rank; direct feedthrough is separate from the state Hankel.
The Static continuation, Theorems 29.4–29.6 and 29.8 consumes the algebraic factorization with continuous derivative parameters , , . The derivative moments are , so the block Hankels differ by an invertible diagonal sign congruence. The strictly proper zero-state task forces the competing direct feedthrough to vanish. Competitors are real finite-dimensional LTI systems and need not be symmetric.
This correspondence does not turn exact moments into samples or transfer the paper’s statistical bounds without its hypotheses. The original Ho–Kalman article is historical attribution, not a separately checked full-text source here. Only the inspected modern paper’s specified statements are used; no article text or figures are reproduced.