On robust PI-control of infinite-dimensional systems

A PI-controller is applied to a class of linear multivariable infinite-dimensional minimum-phase systems satisfying a generalized “relative-degree one” condition. It is shown that the closed-loop system is stable and tracks asymptotically constant reference signals in the presence of asymptotically constant disturbances, provided that the controller gains are sufficiently large. It turns out that the closed-loop system has nice robustness properties under high-gain conditions. In particular, robustness criteria for external and internal stability are given if the closed-loop system is subjected to perturbations induced by nonlinearities in the feedback loop. The analysis is based on frequency-domain as well as state-space methods.