Absolute-stability results in infinite dimensions

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.