Stability of time-varying systems in the absence of strict Lyapunov functions

When a non-linear system has a strict Lyapunov function, its stability can be studied using standard tools from Lyapunov stability theory. What happens when the strict condition fails? This paper provides an answer to that question using a formulation that does not make use of the specific structure of the system model. This formulation is then applied to the study of the asymptotic stability of some classes of linear and non-linear time-varying systems.Peer ReviewedPostprint (author's final draft