2012/10/01 by Marie Frentz, Frentz, Marie, Amol Sasane +1
Mathematics · #46J15 (Secondary) #93B36 (Primary) 93D09 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Optimization and Control (math.OC) #math.FA #math.OA #math.OC #msc:46J15 #msc:93B36 #msc:93D09
paper · pdf · doi:10.48550/arxiv.1210.0402
17 pages
arxiv created 2013/01/11 · arxiv updated 2013/01/14
The classical nu-metric introduced by Vinnicombe in robust control theory for rational plants was extended to classes of nonrational transfer functions in Ball and Sasane [Complex Analysis and Operator Theory; 2012]. In Sasane [Mathematics of Control and Related Fields; 2012], an extension of the classical nu-metric was given when the underlying ring of stable transfer functions is the Hardy algebra, Hinfty. However, this particular extension to Hinfty did not directly fit in the abstract framework given in Ball and Sasane [CAOT 2012]. In this paper we show that the case of Hinfty also fits into the general abstract framework in [BS CAOT 2012] and that the nu-metric defined in this setting is identical to the extension of the nu-metric defined in Sasane [MCRF 2012]. This is done by introducing a particular Banach algebra, which is the inductive limit of certain C*-algebras.