Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control

We derive absolute stability results for well-posed infinite-dimensional sy stems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an expo nentially stable well-posed infinite-dimensional system and an integrator a nd the nonlinearity phi satisfies a sector condition of the form [phi (u), phi (u) - au] less than or equal to 0 for some constant a > 0. These result s are used to prove convergence and stability properties of low-gain integr al feedback control applied to exponentially stable, linear, well-posed sys tems subject to actuator nonlinearities. The class of actuator nonlineariti es under consideration contains standard nonlinearities which are important in control engineering such as saturation and deadzone.