On stability guarantees under sampling for retarded nonlinear systems

In this paper we deal with sampled-data implementation of Lipschitz on bounded sets global asymptotic stabilizers for retarded nonlinear systems, described by Lipschitz on bounded sets functions. We show, with no particular assumption nor requiring exhibition of any Lyapunov–Krasovskii functional, that fast sampling always ensures stabilization in the sample-and-hold sense. That is, for any ball of the origin of initial states and for any final target ball of the origin, there exists a suitably small sampling period such that all solutions starting in the former ball are driven into the latter one, with uniform overshoot and uniform settling time. Global asymptotic and locally exponentially stabilizers are also investigated, showing in this case semi-global uniform convergence to the origin under fast sampling.