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The classical nu-metric introduced by Vinnicombe in robust control theory forrational plants was extended to classes of nonrational transfer functions inBall and Sasane [Complex Analysis and Operator Theory; 2012]. In Sasane[Mathematics of Control and Related Fields; 2012], an extension of theclassical nu-metric was given when the underlying ring of stable transferfunctions is the Hardy algebra, H^infty. However, this particular extension toH^infty did not directly fit in the abstract framework given in Ball and Sasane[CAOT 2012]. In this paper we show that the case of H^infty also fits into thegeneral abstract framework in [BS CAOT 2012] and that the nu-metric defined inthis 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 isthe inductive limit of certain C*-algebras.

Reformulation of the extension of the $\nu$-metric for $H^{\infty}$