2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62800A notion of "asymptotic Cauchy gain" for input/output systems, and an associated small-gain principle, are introduced. A Lyapunov-like characterization allows the computation of these gains for state-space systems, and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops.Preliminary Report. See http://www.math.rutgers.edu/~sontag for related materialsOptimization and Control93B52;93D20;35B35text