Absolute stability results for well-posed infinitedimensional systems with applications to low-gain control

Abstract. We derive absolute stability results for well-posed innite-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 innite-dimensional system and an integrator and the nonlinearity satises a sector condition of the form h(u); (u) − aui 0 for some constant a> 0. These results are used to prove convergence and stability properties of low-gain integral feedback 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