Examples of output regulation for distributed parameter systems with infinite dimensional exosystem

In this short paper we give an example to demonstrate that the geometric theory of output regulation can be adapted to solve a problem of output regulation for a plant consisting of a boundary controlled distributed parameter system with unbounded input and output maps and a signal to be tracked, generated by an infinite dimensional exosystem. The exosystem is neutrally stable but with an infinite (unbounded) set of eigenmodes distributed along the imaginary axis. The usual methods of analysis of the output regulation problem do not apply.