This dissertation presents a discussion of the asymptotic behavior and estimation structure of the H_∞ central controllers in terms of the well-known behavior of the LQG controller and gives some insight into the physics of the H_∞ controller that is often presented in an unclear manner in the current literature. The connections to LQ game theory that underlie this confusion are discussed. Augmented systems that are typically used in disturbance rejection problems are also analyzed. Additionally, a controlled output equation for disturbance rejection is developed based on the physics of the problem rather than the typical ad hoc approaches of the past. These controlled output equations are also appropriate for LQG compensators. In order to verify the proposed approach, an experiment in harmonic and narrowband disturbance rejection using a simply supported steel plate is presented. Discrete-time LQG, and continuous-time H_∞ and LQG controllers that have been transformed to discrete-time are used to determine the attainable performance of each approach. The results indicate that the H_∞ controller provides more damping than either LQG approach and that discrete-time design procedures are necessary for maximum disturbance rejection.