Robust Output Regulation for Continuous-Time Periodic Systems

We consider controller design for robust output tracking and disturbance rejection for continuous-time periodic linear systems with periodic reference and disturbance signals. As our main results, we present four different controllers: a feedforward control law and a discrete-time dynamic error feedback controller for output tracking and disturbance rejection, a robust discrete-time feedback controller, and finally a discrete-time feedback controller that achieves approximate robust output tracking and disturbance rejection. The presented constructions are also new for time-invariant finite and infinite-dimensional systems. The results are illustrated with two examples: a periodically time-dependent system of harmonic oscillators and a nonautonomous two-dimensional heat equation with boundary disturbance.