R. F. Curtain, H. Logemann and O. Staffans

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 $L^2$-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 $L^2$-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 Mathematical Subject Classification: 45M05, 45M10, 93B52, 93C10, 93C20, 93C25, 93D05, 93D09, 93D10, 93D25.

Keywords: iterion, infinite-dimensional systems, integral control, Popov criterion, positive-real, sensor non-linearities, tracking.

E-mail: hl@maths.bath.ac.uk (H. Logemann -- corresponding author)