A refinement of the generalized chordal distance

Abstract

For single input single output systems, we give a refinement of the generalized chordal metric. Our metric is given in terms of coprime factorizations, but it coincides with the extension of Vinnicombe's nu-metric given in earlier work by Ball and Sasane if the coprime factorizations happens to be normalized. The advantage of the metric introduced in this article is its easy computability (since it relies only on coprime factorizations, and does not require normalized coprime factorizations). We also give concrete formulations of our abstract metric for standard classes of stable transfer functions.