Loop recovery and robust state estimate feedback designs

The loop recovery technique has been generalized for nonminimum-phase plants in the following sense. The open-loop properties of certain partial state feedback designs are recovered in a state estimation feedback controller design involving the addition of fictitious plant noise. The partial state is the state of a minimum-phase factor in a minimum-phase, all-pass factored form model. Of course, robust designs are expected only when these are achieved for the case of partial state feedback of only the minimum-phase factor states. This may not always be possible. For the case of minimum-phase plants, known designs and theory are recovered as a special case. The theory and designs of this note generalize to include frequency shaping of both the control objectives and the loop recovery.