Beyond the stability

The paper states Theorem 1 and Theorem 2 precisely with conditions (5)–(8) and the claimed uniform stability, uniform asymptotic stability, and global uniform asymptotic stability conclusions, but it does not provide self-contained proofs of these two main theorems; instead, it offers a corollary showing how Matrosov’s conditions can be used to construct a pair (V, W*) that satisfies Theorem 2, and an illustrative example. The theorem statements appear in the discussion section, but only the corollary is proved (the proof concludes with “This completes the proof.”), and that proof pertains to the corollary, not to Theorem 1 or Theorem 2 themselves . The candidate solution supplies a standard Lyapunov-based proof that is logically complete under the paper’s assumptions, establishing uniform stability from (5)–(7), uniform attractivity from (8) via an integral estimate and a positive-definiteness margin, and GUAS when V1 is radially unbounded; its argument is correct and fills in the missing steps. The example in the paper is consistent with the framework and shows how to bound the tail integral of max{W*,0} in practice .