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H2-optimal model reduction of MIMO systems P. Van Dooren
 

Summary: H2-optimal 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 H2-norm 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
H2-norm as approximation criterion. Since a transfer function has an unbounded H2-norm 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 state-space realizations (A, B, C) RN2
×RNm
×RpN
and (A, B, C) Rn2
× Rnm

  

Source: Absil, Pierre-Antoine - Département d'ingénierie Mathématique, Université Catholique de Louvain

 

Collections: Mathematics