Reformulation of the extension of the $ν$-metric for $H^{\infty}$

Marie Frentz; Amol Sasane

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arXiv · 1210.0402

Reformulation of the extension of the $ν$-metric for $H^{\infty}$

Marie Frentz·Amol Sasane

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Abstract

The classical nu-metric introduced by Vinnicombe in robust control theory for rational plants was extended to classes of nonrational transfer functions in Ball and Sasane [Complex Analysis and Operator Theory; 2012]. In Sasane [Mathematics of Control and Related Fields; 2012], an extension of the classical nu-metric was given when the underlying ring of stable transfer functions is the Hardy algebra, H^infty. However, this particular extension to H^infty did not directly fit in the abstract framework given in Ball and Sasane [CAOT 2012]. In this paper we show that the case of H^infty also fits into the general abstract framework in [BS CAOT 2012] and that the nu-metric defined in this setting is identical to the extension of the nu-metric defined in Sasane [MCRF 2012]. This is done by introducing a particular Banach algebra, which is the inductive limit of certain C*-algebras.

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BibTeX RIS

Marie Frentz, Amol Sasane. 2013-01-11. Reformulation of the extension of the $ν$-metric for $H^{\infty}$. https://arxiv.org/abs/1210.0402

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