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

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


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