Extension of the ν-metric: the H∞ Case
An abstract 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.T his example links the abstract ν-metric with the one proposed by Vinnicombe as a candidate for the ν-metric for nonrational plants.
Keywordsν-metric robust control Hardy algebra quasianalytic functions
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- 1.J.A. Ball and A.J. Sasane. Extension of the v-metric. Complex Analysis and Operator Theory, to appear.Google Scholar
- 2.R.G. Douglas. Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179, Springer-Verlag, New York, 1998.Google Scholar
- 3.R.G. Douglas. Banach algebra techniques in the theory of Toeplitz operators. Expository Lectures from the CBMS Regional Conference held at the University of Georgia, Athens, Ga., June 12-16, 1972. Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 15. American Mathematical Society, Providence, R.I., 1973.Google Scholar
- 4.J.B. Garnett. Bounded analytic functions. Revised first edition. Graduate Texts in Mathematics, 236. Springer, New York, 2007.Google Scholar
- 5.N.Ya. Krupnik. Banach algebras with symbol and singular integral operators. Translated from the Russian by A. Iacob. Operator Theory: Advances and Applications, 26. Birkhäuser Verlag, Basel, 1987.Google Scholar
- 6.N.K. Nikolski. Treatise on the shift operator. Spectral function theory. With an appendix by S. V. Khrushchëv and V. V. Peller. Translated from the Russian by Jaak Pee-tre. Grundlehren der Mathematischen Wissenschaften, 273. Springer-Verlag, Berlin, 1986.Google Scholar
- 7.N.K. Nikolski. Operators, functions, and systems: an easy reading. Vol. 1. Hardy, Hankel, and Toeplitz. Translated from the French by Andreas Hartmann. Mathematical Surveys and Monographs, 92. American Mathematical Society, Providence, RI, 2002.Google Scholar