Estimates for weighted homogeneous delay systems: A Lyapunov-Krasovskii-Razumikhin approach

The paper proves a KL-type bound via a Lyapunov–Krasovskii comparison (Lemma 7 and Theorems 3/5), using inequalities (15)–(19) and the Razumikhin-inspired condition (23); however, the displayed estimate (20) appears with a positive exponent 1/μ, which conflicts with the decay law of the comparison solution and is almost surely a sign typo. The candidate solution derives the standard Bihari decay bound with exponent −1/μ and then notes the printed (weaker) form follows trivially, while also reconstructing the attraction set via Δα and condition (23). Aside from the sign typo in (20) and omitted proofs of Lemmas 8–9/Theorem 4 in the paper, the logic matches; the candidate’s derivation uses slightly different constants (via convexity/Jensen rather than the paper’s ρ1), but is sound and yields the same structure of estimates. Key steps and constants match the paper’s framework (functional (6), bounds (11)–(13), domain size via H2,H3, and Δα) .