Absolute-stability results in infinite dimensions

Abstract

We derive absolute–stability results of Popov and circle–criterion type for infinite–dimensional systems in an input–output setting. Our results apply to feedback systems in which the linear part is the series interconnection of an input–output stable linear system and an integrator, and the nonlinearity satisfies a sector condition which, in particular, allows for saturation and deadzone effects. We use the input–output theory developed to derive state–space results on absolute stability applying to feedback systems in which the linear part is the series interconnection of an exponentially stable, well–posed infinite–dimensional system and an integrator.