Reduced order LQG design: Conditions for feasibility

This paper starts with a discussion on the Projection of Dynamics-principle as a model reduction tool. This is exploited in modal approximations and reductions based on open loop balancing. Similar ideas can be employed for the reduction of the closed loop, terminal controller problem, in the presence of noise, leading to the LQG balanced realizations. An interpretation of the various terms in the optimal performance index leads to the motivation for this reduction technique. It is shown that several "natural" restrictions occur, constraining the faithfulness of this reduction technique. As in the open loop case, it illustrates the insufficiency of the canonical riccation towards the determination of the reduced order models.