Loop transfer recovery techniques for discrete-time optimal regulators using prediction estimators

For discrete-time LQG optimal regulators using current estimators, it has been shown that perfect recoveries of the loop transfer matrices at the input or at the output are possible for square minimum-phase systems. However, current estimators cannot be used when the processing time of the controller is significant. In this note, the loop transfer recoveries using prediction estimators for square minimum-phase systems are considered. It is shown that, although the perfect recoveries are impossible, the feedback properties obtained by the recovery techniques are those that can be recovered best in the presence of the delay in the controller.