Robust output stability and input-to-output stability based on output dissipation

LaSalle techniques to ensure the convergence of a given output usually fail at guaranteeing uniform convergence time, which induces robustness issues. Recent works have provided extra conditions under which a Lyapunov function that dissipates in terms of only the output guarantees this uniformity. In this paper, we extend these results to systems with inputs in order to establish either robust stability or input-to-output stability. In addition, we show that a recent relaxation of Barb__lat's lemma is also applicable to systems with inputs. The significance of the proposed results is demonstrated in the context of a recent adaptive control scheme.