Nonlinear Criteria for Stability of Nonautonomous Dynamics - A New Zabczyk-Rolewicz Type Approach

We present new Zabczyk-Rolewicz type methods of exploring the uniform exponential stability of nonautonomous dynamics.First, we give a characterization of Zabczyk type for uniform exponential stability of discrete nonautonomous systems.Next, we obtain a new criterion of Zabczyk-Rolewicz type for uniform exponential stability, using general nonlinear trajectories.In addition, we discuss consequences for uniformly bounded discrete nonautonomous systems.Furthermore, we apply our results to deduce the famous stability theorem of Rolewicz for continuous-time dynamics.