Distributed Lyapunov Functions for Nonlinear Networks

The paper’s augmented comparison lemma (its Lemma 2) is correct, though tersely justified via a citation. The candidate solution supplies a standard, fully detailed semigroup/Metzler proof of the same lemma and then gives a constructive choice V_p = k V_c that satisfies the derivative inequality required in the paper’s Theorem 1. While the paper’s proof sketch for Theorem 1 is brief and conflates steps (it does not explicitly construct V_p), the stated inequality (8) follows directly from substituting R = 1_L V_c − V into V̇ ≤ AV + BR, and the model provides an explicit family V_p that meets it. Thus both are correct; the model offers a clearer proof and construction.