Observability of Nonlinear Dynamical Systems over Finite Fields

Ramachandran Ananthraman, Virendra Sule

wronghigh confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s core constructions (Koopman-restricted LOR, injectivity criterion) are sound, but Theorem 3 overclaims: it states the maximum number of output samples needed equals N (the LOR dimension). The proof only establishes a uniform upper bound of N via Cayley–Hamilton; in general the observability index can be strictly smaller than N (e.g., when Γ has full column rank). The candidate model gives a correct, sharper statement: N samples always suffice uniformly and the bound is tight in general (e.g., single-output Jordan block). The model’s linear-algebraic proof of LOR observability is also more precise than the paper’s informal argument.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript develops a Koopman-based linear output realization that reproduces outputs of a nonlinear DSFF and offers an elegant injectivity-based observability criterion. However, the sample-complexity claim is overstated: the argument given proves a uniform upper bound of N time steps, not equality for arbitrary observable systems. Strengthening rigor (notably for Lemma 1) and correcting Theorem 3’s statement or adding qualifying assumptions/examples are necessary. With these revisions, the contribution will be solid and useful.