On global uniform asymptotic stability of nonlinear time-varying systems in cascade

Abstract

In this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade. In particular, we give sufficient conditions to guarantee that (i) a globally uniformly stable (GUS) nonlinear time-varying (NLTV) system remains GUS when it is perturbed by the output of a globally uniformly asymptotically stable (GUAS) NLTV system, under the assumption that the perturbing signal is absolutely integrable; (ii) if in addition the perturbed system is GUAS, it remains GUAS under the cascaded interconnection; (iii) two GUAS systems yield a GUAS cascaded system, under some growth restrictions over the Lyapunov function. Our proofs rely on the second method of Lyapunov, roughly speaking on a “δ-ε stability analysis”.