On the Time-Discretization of Singularly Perturbed Uncertain Systems

Abstract

Uncertain dynamical systems with two time scales are under consideration. The ratio of the magnitudes of the multi-valued vector fields related to the slow and fast subsystems is given as a singular perturbation parameter. The averaging method is employed in order to construct a limiting system for the slow subsystem, representing the case of a vanishing perturbation parameter. This method is a classical one in connection with continuous time systems, but works as well for uncertain systems in discrete time. However, the relation between a continuous time system and its time-discretized version along with the limiting behavior as the perturbation tends to zero has not yet been elaborated. In the present work it is shown that both limiting procedures, the vanishing singular perturbation parameter and the vanishing discretization step, are commutable.