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

Abstract

An abstract $ν$-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 important concrete special instance of the abstract $ν$-metric, by verifying that all the assumptions demanded in the abstract set-up are satisfied when the ring of stable transfer functions is the Hardy algebra $H^\infty$. This settles the open question implicit in \cite{BalSas2}.