Comparison of two LQG-based methods for disturbance rejection

When the disturbances acting on a system reflect the dynamics of the process generating them (i.e. disturbances other than white noise), this information can be exploited for the design of disturbance rejection controllers. Two modern control approaches for designing linear disturbance rejection controllers are discussed: disturbance modeling and frequency shaping of cost functionals. Both methods are extensions of linear-quadratic-Gaussian theory. It is shown that although the philosophies used to develop the two control schemes are very different, there is a distinct relationship between them. This is formalized by showing that the two methods are equivalent for the single-input-single-output case. The duality of the two methods is discussed for the multi-input-multi-output case