The robust stability analysis of asynchronous and uncertain sampled-data systems with constant incremental input delay is addressed in the looped-functional framework. These functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discrete-time stability conditions in an affine way, enabling then the consideration of uncertain and time-varying systems. The stability conditions are obtained by first reformulating the sampled-data system as an impulsive system, and by then considering a tailored looped-functional along with Wirtinger's inequality, a recently introduced inequality that has been shown to be less conservative than Jensen's inequality. Several examples are given for illustration.