Finite model order optimal input design for minimum variance control

It is well known that if we intend to use a minimum variance controller to stabilize a minimum phase plant (with exactly one time delay), which is designed based on a model obtained from an identification experiment, the best experiment which can be performed on the system to determine such a model (subject to output power constraints, or for some specific model structures) is to use the true minimum variance controller. This result has been derived under several circumstances, first using asymptotic (in model order) variance expressions but also more recently for ARMAX models of finite order. In this paper we re-approach this problem by using a recently developed geometric approach to variance analysis, which is non asymptotic in model order, with which we generalize some of the previous results established in the literature. We also believe the new derivations to be more transparent than earlier contributions.