Averaging Method for One-Sided Lipschitz Differential Inclusions with Generalized Solutions

Abstract

We investigate the convergence of the solution set for singularly perturbed differential inclusions using an averaging technique. The limits of the fast solutions are considered as generalized solutions (i.e., Radon probability measures) of the degenerate system. Exploiting in addition the one-sided Lipschitz condition we prove the existence of a limit of the solution set inan appropriate topology.