On input-to-state stability for time varying nonlinear systems

Input-to-state stability was introduced about 10 years ago. This notion is nowadays a central concept in the analysis of nonlinear systems. However, most theoretical developments dealt mainly with time invariant systems. In this work we study the Lyapunov characterizations of input-to-state stability for time varying nonlinear systems, and in particular, for periodic time varying systems. We also present a small gain theorem for time varying nonlinear systems.