Output regulation for delay systems: tracking and disturbance rejection for an oscillator with delayed damping

In this paper we apply the methods of geometric output regulation to regulate a linear control system with a delay. For this example our design objective is to track a harmonic reference signal and while rejecting a constant disturbance. The signal to be tracked and disturbance to be rejected are generated by a finite dimensional exogenous system. The main purpose of this work is to demonstrate, for an interesting example, the form and simple solution of the "regulator equations" for delay equations.