High Gain Observers and Hybrid Output Regulation

We consider the hybrid output regulation problem for minimum phase linear systems with relative degree greater than one. In the hybrid output regulation problem, an exosystem provides a disturbance or tracking signal that must be matched via an internal model in order to asymptotically regulate the error. This hybrid exosystem is a linear system that experiences periodic jumps. In this context, we build upon previous works in hybrid output regulation by showing how high-gain observers can successfully overcome the obstacle of high relative degree. In certain scenarios, they can also be used to stabilize the hybrid internal model dynamics through jumps.