Global Stability Notions to Enhance the Rigor and Robustness of Adaptive Control

Both the paper and the model prove the same LaSalle-like p-OAG result under hypotheses (115)–(116). The paper states p-OAG and Theorem 9 explicitly and concludes α=b(0), γ(s)=b(s)−b(0) (the definition and theorem statement are in the notes, and the proof derives (118)–(120) and invokes Barbălat’s lemma to obtain limsup|y|≤b(∥d∥∞) . The candidate argument follows the same chain (dissipation inequality, boundedness of Hs on bounded trajectories, uniform continuity of Qs(x(t)), Barbălat, then limsup bound), differing only in using an ω-limit-set argument instead of the paper’s direct contradiction step. Hence the proofs are substantively the same and correct.