On two projection related properties of the L/sub 2/ optimal reduced order model

The paper investigates reduced order models obtained by projection of a high order system, and presents two properties of optimal L/sub 2/ reduced order models. It deals first with the existence and uniqueness of a projection that relates the given full order and reduced order systems. Then it is shown that in cases where not all models of a certain order can be obtained by a projection, the optimal L/sub 2/ reduced order model is obtained by a unique projection, which resides on the boundary of the set of attainable models. Another result that is presented is matrix inequalities that characterize the optimal projection.