Extension of the $ν$-metric: the $H^\infty$ case

An abtract $ν$-metric was introduced by Ball and Sasane, with a view towards extending the classical $ν$-metric of Vinnicombe from the case of rational transfer functions to more general nonrational transfer function classes of infinite-dimensional linear control systems. In this short note, we give an additional concrete special instance of the abstract $ν$-metric, by verifying all the assumptions demanded in the abstract set-up. This example links the abstract $ν$-metric with the one proposed by Vinnicombe as a candidate for the $ν$-metric for nonrational plants.

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