Regular Pairings for Non-Quadratic Lyapunov Functions and Contraction Analysis

Anton V. Proskurnikov, Francesco Bullo

correcthigh confidence

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

Audit review

The paper’s Theorem 3.6 states the equivalence of properties (i)–(vii) for weak pairings compatible with a norm and proves it via a chain (i)⇒(ii)⇒(iii)⇒(iv)⇒(i) plus equivalence of (v),(vi) and linkage to (i)–(iv). The candidate’s solution establishes the same equivalences, with essentially identical arguments for (i)⇔(ii), (ii)⇒(iii), (iii)⇒(iv), and (vi)⇒(v); it differs mainly in proving (v)⇒(vii) by an exponential semigroup argument and then closing the cycle with (vii)⇒(i). The logical steps align with the statements and lemmas in the paper, and any minor technicalities (e.g., exchanging lim and sup in (v)⇒(vii)) are standard and readily justified.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper provides a robust equivalence theorem that unifies multiple semi-inner product notions relevant to contraction analysis. Proofs are correct and connect well with established theory. The presentation is clear overall, but a couple of standard steps could be made more explicit to improve self-containment.