Abstract
The problem of approximating a given, possibly infinite dimensional, transfer function, by one of prescribed McMillan degree is considered. Firstly lower bounds on the achievable error are given for a variety of norms (L∞ and freauency L∞ weighted L∞ for the transfer function, L1 for the impulse response, largest singular value, Hilbert-Schmidt and nuclear norms for the Hankel operator). Upper bounds are derived for the optimal Hankel norm method, truncated balanced realizations, modal expansions and some frequency weighted methods. These all involve singular values of Hankel operators and the asymptotic behaviour of these singular values is analysed for infinte dimensional systems. Finally improved estimates of the achievable L∞-error are studied.
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