Interaction Identification of a Heterogeneous NDS with Quadratic-Bilinear Subsystems

The paper’s Theorem 2 asserts that cosine/sine Cesàro-averaged products of uniformly sampled outputs recover sums of the real/imaginary parts of tangential interpolation vectors over aliasing index sets S[r] and S[i]. Its proof (Appendix) expands the steady-state as a discrete spectrum indexed by all finite sums of PSGS eigenvalues (eqs. (18)–(19)), shows transients vanish under stability and imaginary-axis PSGS (A18–A20), and evaluates the discrete-time averages via a closed-form summation lemma (eqs. (20)–(23)) to obtain the limits (24)–(25) . The candidate solution reproduces the same structure: spectral expansion via generalized TFMs, separation of transient/steady-state, and Cesàro orthogonality/aliasing to isolate the lines at ±Ω, summing conjugate contributions to Re/Im parts. Differences are stylistic (e.g., invoking almost-periodicity/Fejér), not substantive. Both are correct given Assumptions 1–5; a common minor gap is that neither fully quantifies interchange of limit and infinite sums, though the paper later notes exponential decay of high-order terms under a small resolvent condition for practical estimation .