A feedforward–feedback controller for infinite-dimensional systems and regulation of bounded uniformly continuous signals

We design a controller for infinite-dimensional linear systems (with bounded control, observation and feedthrough operators) which, under certain assumptions, achieves asymptotic tracking of arbitrary bounded uniformly continuous reference signals in the presence of disturbances. The proposed controller is of feedforward–feedback type: The dynamic feedback part is used to stabilize the closed-loop system consisting of the plant and the controller, whereas the feedforward part is tuned using the regulator equations to achieve the regulation of desired signals. We also completely solve the regulator equations for SISO systems, and we discuss robustness properties of the proposed controller. A useful feature in our design is that the feedforward part of the controller can be designed independently of the feedback part. This automatically leads to a degree of robustness in the stabilizing part of the controller, which is not present in the existing state feedback controllers solving the same output regulation problem.