2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63958Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of attraction of the unforced system, must also converge to the equilibrium. This "well-known" but hard-to-cite fact is proved and slightly generalized here.See http://www.math.rutgers.edu/~sontag for related workOptimization and Control93D20;34D20;58F10text