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 that exhibit both parametric and dynamic modelling 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. Ii-optimal control). While asymptotic performance is guaranteed, we also provide bounds that quantify the transient response behaviour of this particular control scheme.