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doi:10.1016/0167-6911(94)00003-E 
Copyright © 1995 Published by Elsevier Science B.V.
An equivalence between rational H2 and Hankel-norm approximations
Received 14 September 1993;
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Abstract
Let H(z) be a given function in H2 A classical problem in engineering analysis is to find a rational function G (z) ε H2 degree M say, which is closest to H(z) in 2-norm. This problem is typically approached using the cost function |H(z) − G(z)|2, in which G(z) is allowed to vary over the set of Mth-order rational functions in H2 and for which stationary points are sought. We show that each stationary point of degree M of this functional coincides with a weighted Hankel-norm approximant to H(z). The weighting function derives from the outer factor of the error function H(z) − G(z) stationary point of the rational H2 approximation problem.
Author Keywords: Rational H2 approximation; Hankel-norm approximation; Model reduction; Stationary points
