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SIAM J. MATRIX ANAL. APPL. c 2010 Society for Industrial and Applied Mathematics
Vol. 31, No. 5, pp. 27382753
H2-OPTIMAL MODEL REDUCTION WITH HIGHER-ORDER POLES
PAUL VAN DOOREN, KYLE A. GALLIVAN, AND P.-A. ABSIL
Abstract. We revisit the problem of approximating a multiple-input multiple-output p × m
rational transfer function H(s) of high degree by another p × m rational transfer function H(s) of
much smaller degree, so that the H2-norm of the approximation error is minimized. We show that
in the general case of higher-order poles in the reduced-order model, called the defective case, the
stationary points of the H2-norm of the approximation error can still be characterized by tangential
interpolation conditions. We also indicate that the sensitivity of the solution of this problem depends
on the parameterization used.
Key words. model reduction, optimal H2 approximation, tangential interpolation
AMS subject classifications. 41A05, 65D05, 93B40
1. Introduction. In this paper, we 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
the approximation criterion. We refer to  for the relevant background on model
reduction and linear system theory.