Global uniform asymptotic stability of cascaded non-autonomous nonlinear systems

In this short paper we deal with the stability analysis problem of cascaded non autonomous nonlinear systems. In particular we answer to the following questions: (1) What happens with the solutions of a time varying nonlinear system which is globally uniformly stable when it is perturbed by the output of a globally exponentially stable system (GES), in particular, when both systems form a cascade?. (2) If a time varying nonlinear system is globally uniformly asymptotically stable (GUAS), is this stability property preserved when it is perturbed by an exponentially decaying input?, (3) Under which conditions the cascaded interconnection of two GUAS non autonomous nonlinear systems, is still GUAS?.