We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator and the nonlinearity φ satisfies a sector condition of the form φ(u), φ(u) − au ≤ 0 for some constant a > 0. These results are used to prove convergence and stability properties of low-gain integral

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... edback control applied to exponentially stable, linear, well-posed systems subject to actuator nonlinearities. The class of actuator nonlinearities under consideration contains standard nonlinearities which are important in control engineering such as saturation and deadzone. AMS Subject Classification. 93C10, 93C20, 93C25, 93D05, 93D09, 93D10, 93D21.