Geometrical Properties of the L2 Optimal Order Reduction Projection

The paper investigates reduced order models obtained by projection of a high order system, and presents two properties of the optimal L₂ reduced order models. It deals first with existence and uniqueness of a projection that relates given full order and reduced order systems. The analysis is carried out by investigating the properties of the Kronecker canonical form of a certain matrix pencil. Then it is shown that for the optimal L₂ reduced order model the pencil assumes a non-generic structure, and that in turn indicates that the corresponding projection is discontinuous at that point and in some cases resides on the boundary of the set of attainable models