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Super-optimal Hankel norm approximations

  • N. J. Young
Part of the NATO ASI Series book series (volume 34)

Abstract

For any m × n rational transfer function matrix F and any nonnegative integer k there exista a unique rational function having at most k unstable poles and Minimising s (F - F̄): that is, minimising the sequence (s 0 (F - F̄), s 1 (F - F̄),...) with respect to the lexicographic ordering, where
$$ s{j^\infty }(G)\,:\, = \mathop {\sup }\limits_{\left| z \right| = 1} \;sj(G(z)) $$
(1)
and s j (.) denotes the jth singular value of a matrix.

Keywords

Hankel Operator Transfer Function Matrix Rational Transfer Function MCMillan Degree High Level Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • N. J. Young
    • 1
  1. 1.Department of Mathematics, University GardensUniversity of GlasgowGlasgowScotland

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