Equivalence of disturbance observer structures for linear systems

Several techniques exist to incorporate disturbance rejection requirements in a linear controller design. Contrary to, for example the H-infinity controller design technique where only one degree of freedom is available to obtain both disturbance rejection and performance, a disturbance observer adds a degree of freedom, thereby enabling a separate design of the disturbance rejection and the performance. There are many ways to design, implement and represent disturbance observers. We focus on two design methodologies and their corresponding representations. It can be shown that, in the case that the (SISO) plant is linear, the methodologies result in an equivalent disturbance observer. We use this equivalence to relate some properties well-known for one methodology to the other methodology, and vice versa