Extension of the ν-metric: the H^∞ case

2010/10/09 by Joseph A. Ball, Ball, Joseph A., Amol J. Sasane +1
Mathematics · #46J15 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Primary 93B36 #Rings and Algebras (math.RA) #Secondary 93D15 #math.CV #math.FA #math.OC #math.RA #msc:46J15 #msc:93B36 #msc:93D15

paper · pdf · doi:10.48550/arxiv.1010.1843

8 pages

arxiv created 2010/10/09 · arxiv updated 2010/10/12

Abstract

An abtract 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 additional concrete special instance of the abstract ν-metric, by verifying all the assumptions demanded in the abstract set-up. This example links the abstract ν-metric with the one proposed by Vinnicombe as a candidate for the ν-metric for nonrational plants.

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