Optimal asymptotic robust performance through logic-based switching

Abstract

In this paper we introduce a novel measure of asymptotic disturbance rejection for a feedback system. This notion of asymptotic performance is particularly well suited to the robust control of systems which exhibit both parametric and dynamic modeling uncertainty. We then derive a switching type controller that provides optimal asymptotic disturbance rejection properties. The particular notion of disturbance rejection we consider is rejection of persistent bounded disturbances (i.e., l1-optimal control). While asymptotic performance is guaranteed, we also provide bounds that quantify the transient response behavior of this particular control scheme.