Extension of the $\nu$-metric for stabilizable plants over $H^\infty$

Amol Sasane

doi:10.3934/mcrf.2012.2.29

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2012, Volume 2, Issue 1: 29-44. Doi: 10.3934/mcrf.2012.2.29

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Extension of the $\nu$-metric for stabilizable plants over $H^\infty$

Amol Sasane^1,

1.
Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE

Received: July 31, 2011

Revised: September 30, 2011

Published: February 2012

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Abstract

An abstract $\nu$-metric was introduced in [1], with a view towards extending the classical $\nu$-metric of Vinnicombe from the case of rational transfer functions to more general nonrational transfer function classes of infinite-dimensional linear control systems. Here we give an important concrete special instance of the abstract $\nu$-metric, namely the case when the ring of stable transfer functions is the Hardy algebra $H^\infty$, by verifying that all the assumptions demanded in the abstract set-up are satisfied. This settles the open question implicit in [2].

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Mathematics Subject Classification: Primary: 93B36, 93D15; Secondary: 46J15.

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References

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