Stability Results of Popov-Type for Infinite-Dimensional Systems with Applications to Integral Control

Abstract

We derive absolute stability results of Popov-type for infinite-dimensional systems in an input-output setting. Our results apply to feedback systems where the linear part is the series interconnection of an L2-stable linear system and an integrator, and the non-linearity satisfies a sector condition which allows for non-linearities with lower gain equal to zero (such as saturation, or more generally, bounded non-linearities). These results are used to prove convergence and stability properties of low-gain integral feedback control applied to L2-stable linear systems subject to actuator and sensor non-linearities. The class of actuator/sensor non-linearities under consideration contains standard non-linearities which are important in control engineering such as saturation and deadzone. Moreover, we use the input-output theory developed to derive state-space results on absolute stability and low-gain integral control for strongly stable well-posed infinite-dimensional linear systems. 2000 Mathematics Subject Classification 45M05, 45M10, 93B52, 93C10, 93C20, 93C25, 93D05, 93D09, 93D10, 93D25.