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Reformulation of the extension of the ν-metric for H∞

Frentz, Marie and Sasane, Amol (2013) Reformulation of the extension of the ν-metric for H∞. Journal of Mathematical Analysis and Applications, 401 (2). pp. 659-971. ISSN 0022-247X

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Abstract

The classical ν-metric introduced by Vinnicombe in robust control theory for rational plants was extended to classes of nonrational transfer functions in Ball (2012) [1]. In Sasane (2012) [11], an extension of the classical ν-metric was given when the underlying ring of stable transfer functions is the Hardy algebra, H∞. However, this particular extension to H∞ did not directly fit in the abstract framework given in Ball (2012) [1]. In this paper we show that the case of H∞ also fits into the general abstract framework in Ball (2012) [1] and that the ν-metric defined in this setting is identical to the extension of the ν-metric defined in Sasane (2012) [11]. This is done by introducing a particular Banach algebra, which is the inductive limit of certain C*-algebras

Item Type: Article
Official URL: http://www.journals.elsevier.com/journal-of-mathem...
Additional Information: © 2013 Elsevier
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 24 Jan 2013 12:17
URL: http://eprints.lse.ac.uk/48076/

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