A sufficient condition for asymptotic stability for a class of time-varying parameterized systems

We derive sufficient conditions for local asymptotic stability for a class of parameterized time-varying systems, whose dynamics are in general unbounded in time. Our main result generalizes a well known limiting-dynamics based approach due to Peuteman and Aeyels (1999) in [9] for fast time-varying systems whose dynamics are bounded in time. Its proof is based on a new result providing a Lyapunov characterization for exponential stability.