On stability of sets for sampled-data nonlinear inclusions via their approximate discrete-time models

Abstract

We generalize previous results on stability of sampled-data systems based on the approximate discrete-time models: we consider stabilization of arbitrary closed sets (not necessarily compact), plants described as sampled-data differential inclusions and arbitrary dynamic controllers in the form of difference inclusions. Our result does not require the knowledge of a Lyapunov function for the approximate model, which is a standing assumption in previous papers. We present checkable conditions that one can use to conclude semi-global practical asymptotic (SPA) stability, or global exponential stability (GES), of the sampled-data system via appropriate properties of its approximate discrete-time model. Thus, we provide a framework for stabilization of arbitrary closed sets for sampled-data nonlinear differential inclusions via their approximate discrete-time models.