Optimal Modal Truncation

The paper formulates H2-optimal modal truncation as a convex quadratic binary program over selection variables α with realness constraints Mα = 0, proves that any finite-H2 solution must satisfy Dα = D, and shows the squared H2-error equals (1−α)^T Q (1−α) with Q_{ij} = tr(Φ_i Φ_j^H)/(-λ_i − λ_j^*) (Theorem 1), exactly matching the candidate’s derivation and final program . The setup—DCF, stability, semisimple poles—is consistent with the paper’s assumptions . Minor presentational differences remain: the paper emphasizes Hermitian Q (and calls the objective a squared norm), while the candidate also notes Q is a Gram matrix in H2 and hence PSD; both lead to the same optimization and constraints.