Note on input-to-state stability of sampled-data nonlinear systems

Abstract

It is shown for nonlinear systems that sampling sufficiently fast an input-to-state stabilizing (ISS) continuous time control law results in an ISS sampled-data control law. Two main features of our approach are: we show how the nonlinear sampled-data system can be modeled by a functional differential equation (FDE); we exploit a Razumikhin type theorem for ISS of FDE that was recently proved in [14] to analyze the sampled-data system.