On Algebraic and Linear Algebraic Aspects of Co-Order Three H2 Model Order Reduction

We present an algebraic method to compute a globally optimal H2 approximation of order N-3 to a given system of order N. First, the problem is formulated as a two-parameter polynomial eigenvalue problem with a special structure. To solve it, we apply and generalize algebraic techniques used in the computation of the Kronecker canonical form of a matrix pencil. Finiteness of the number of nontrivial solutions then allows the problem to be reduced to a one-parameter polynomial eigenvalue problem, which is solved with standard numerical methods. An example demonstrates the approach and provides a proof of principle.