Lyapunov Function for the Nonlinear Moog Voltage Controlled Filter

Stefan Bilbao

incompletehigh confidence

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

Audit review

The paper’s Lyapunov construction and scaling are sound for 0 < α < √2, but its proof of strict negativity (C3′) quietly switches a strict bound to a non-strict one at α = √2, so negative definiteness is not established on the boundary (r = 1). The candidate solution mirrors the paper’s Lyapunov function but relies on an incorrect inequality to upper-bound −d^2 b4 a4 by −(d^2/2) b4^2, which fails for α > 1; it also asserts b4 a4 > b4^2 for α = 1, which is false. Net: the paper underspecifies the boundary case (and omits α = 0 in the main line), and the model’s proof has a critical inequality error.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper introduces a concise and useful Lyapunov function with an insightful scaling that convincingly yields strict decay for 0 < α < √2. However, at α = √2 the argument relaxes a strict inequality to a non-strict one, so negative definiteness (and hence C3′) is not established as written at the boundary; the text nonetheless claims full-range asymptotic stability. This can be corrected by a tighter bound, an invariance-based argument, or by explicitly limiting the claim at r = 1. A brief note on α = 0 would also match the stated “full range.”