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

An abstract ν-metric was introduced in [1], 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. Here we give an important concrete special instance of the abstract ν-metric, namely the case when the ring of stable transfer functions is the Hardy algebra H, by verifying that all the assumptions demanded in the abstract set-up are satisfied. This settles the open question implicit in [2].