ON STABILITY OF SETS FOR SAMPLED-DATA NONLINEAR INCLUSIONS VIA THEIR APPROXIMATE DISCRETE-TIME MODELS AND SUMMABILITY CRITERIA

Abstract

This paper consists of two main parts. In the first part, we provide a framework for stabilization of arbitrary (not necessarily compact) closed sets for sampled-data nonlinear differential inclusions via their approximate discrete-time models. We generalize [D. Nešiĉ, A. R. Teel, and P. V. Kokotović, Systems Control Lett., 38 (1999), pp. 259-270, Theorem 1] in several different directions: we consider stabilization of arbitrary closed sets, 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 i..