Extension of the $\nu$-metric

TL;DR

This paper extends the $ u$-metric from robust control theory to encompass infinite-dimensional systems and nonrational transfer functions, broadening its applicability.

Contribution

The paper introduces an extension of the $ u$-metric to infinite-dimensional and nonrational transfer functions, expanding its use in control theory.

Findings

Extended the $ u$-metric to infinite-dimensional systems

Applicable to classes of nonrational transfer functions

Broadened the scope of robust control analysis

Abstract

We extend the $\nu$-metric introduced by Vinnicombe in robust control theory for rational plants to the case of infinite-dimensional systems/classes of nonrational transfer functions.