Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral 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 formh(u);(u) aui0 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.