Structure-Preserving Model Order Reduction for Index Two Port-Hamiltonian Descriptor Systems

The paper’s Theorem 2 specifies the reduced pH-DAE Σr(θ), asserts it satisfies the pH structure, is index two, and has transfer function Hr(s,θ) = Hp,r(s,θ) + s L(θ)L(θ)^T, with a brief proof using x3 = −ẋ2 = L(θ)^T u̇ (assuming u is differentiable) . The candidate solution provides a compatible, more explicit derivation: it verifies pH structure from the block construction, proves regularity of sEr − (Jr − Rr) by block factorization, exhibits the semi-explicit DAE to read off the index-two constraint, and computes the transfer function via block inversion, recovering the same formula. The model fills in details (notably the regularity proof) that the paper only assumes in context (transfer function well-defined under regularity) . No contradictions found.