 
Summary: H2optimal model reduction of MIMO systems
P. Van Dooren
K. A. Gallivan§
P.A. Absil
Abstract
We consider the problem of approximating a p × m rational transfer function H(s) of high degree
by another p × m rational transfer function bH(s) of much smaller degree. We derive the gradients of
the H2norm of the approximation error and show how stationary points can be described via tangential
interpolation.
Keyword Multivariable systems, model reduction, optimal H2 approximation, tangential interpolation.
1 Introduction
In this paper we will consider the problem of approximating a real p × m rational transfer function H(s) of
McMillan degree N by a real p × m rational transfer function H(s) of lower McMillan degree n using the
H2norm as approximation criterion. Since a transfer function has an unbounded H2norm if it is not strictly
proper (a rational transfer function is strictly proper if it is zero at s = ), we will constrain both H(s) and
H(s) to be strictly proper. Such transfer functions have statespace realizations (A, B, C) RN2
×RNm
×RpN
and (A, B, C) Rn2
× Rnm
