Control of Port-Hamiltonian Differential-Algebraic Systems and Applications

Volker Mehrmann, Benjamin Unger

correctmedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Theorem 6.3 shows that an LTV pHDAE with quadratic Hamiltonian is invariant under the stated coordinate changes z = V \tilde z with premultiplication by U^T, yielding the transformed coefficients Ẽ, Q̃, J̃, R̃, G̃, P̃, K̃ and preserving H as well as skew-adjointness of L and PSD of W̃; the proof hinges on identities like Q̃^T Ẽ = V^T Q^T E V and W̃ = diag(V^T, I) W diag(V, I) . The candidate solution reproduces the same argument with more detailed algebra (explicitly verifying d/dt(Q̃^T Ẽ) via the skew-adjointness identity (4.7)), and reaches identical conclusions. One minor discrepancy is a likely sign typo in the paper’s output term (S + N versus S − N); elsewhere the survey consistently uses (S − N) for linear pHDAEs, so this does not affect the invariance result .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The core invariance result for linear time-varying pHDAEs with quadratic Hamiltonian is correctly stated and proved in the survey, and the candidate solution provides a faithful, detailed derivation that matches the survey’s logic. The only issue is a minor sign inconsistency in the theorem’s output term, which does not affect correctness but should be harmonized with the standard convention used elsewhere in the paper.