The goal of this dissertation is to present a framework and regulator design for output regulation of linear hybrid systems with periodic jump times. The term output regulation is normally used in regards to the problem of regulating an error variable of a system in the presence of an exogenous system (exosystem). This problem comes up in the context of tracking a trajectory or rejecting a disturbance that can be modeled as the output of a dynamical system (the exosystem).

We begin by defining output regulation for this framework and developing a set of hybrid regulation equations and a hybrid internal model property. Following this we provide guidelines for the design of the regulator. The regulator should include an internal model capable of reproducing the output of the exosystem, as well as a stabilizer unit that is designed to make the closed loop system stable. The stabilizer unit used in this dissertation is a high gain stabilizer that utilizes a high gain observer to track unmeasured plant variables. The high gain methods are based on their continuous time counterparts. The internal model is designed with an eye towards general applicability and thus takes advantage of a property called "visibility," so as to reproduce the steady-state trajectory of the exosystem, as opposed to the entire state, which is all that turns out to be necessary in order to achieve output regulation.

This framework of output regulation can be useful in attempting to asymptotically track trajectories that cannot be produced by continuous-time dynamical system, such as a spline trajectory, for which an example is provided. Furthermore, the use of an internal model allows one to achieve robust output regulation. In this context, robust output regulation means maintaining output regulation despite uncertain parameters in the plant.