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2110.11735

Kernel-based models for system analysis

Henk J. van Waarde, Rodolphe Sepulchre

correctmedium confidence
Category
Not specified
Journal tier
Strong Field
Processed
Sep 28, 2025, 12:56 AM

Audit review

The candidate solution reproduces the paper’s main arguments: (i) the RKHS-based Lipschitz bound via Lemma 1 and the nonexpansive-kernel condition; (ii) the representer theorem leading to ĉ=(G+γI)^{-1}ȳ and the norm formula for Ĥ; (iii) causality of Ĥ from causal kernels; and (iv) small-gain conditions ensuring well-posedness, causality, and incremental dissipativity of (N21+N22Ĥ)(N11+N12Ĥ)^{-1}. Aside from a minor slip about coefficient uniqueness (which is ensured by γ>0), the reasoning aligns closely with Theorems 1–4 in the paper.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The solution mirrors the paper’s structure and results, correctly leveraging RKHS machinery, nonexpansive kernels, and scattering-based small-gain arguments to guarantee causality and incremental dissipativity. A few small clarifications would strengthen precision and readability.