\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Extension of the $\nu$-metric for stabilizable plants over $H^\infty$

Abstract Related Papers Cited by
  • An abstract $\nu$-metric was introduced in [1], with a view towards extending the classical $\nu$-metric of Vinnicombe from the case of rational transfer functions to more general nonrational transfer function classes of infinite-dimensional linear control systems. Here we give an important concrete special instance of the abstract $\nu$-metric, namely the case when the ring of stable transfer functions is the Hardy algebra $H^\infty$, by verifying that all the assumptions demanded in the abstract set-up are satisfied. This settles the open question implicit in [2].
    Mathematics Subject Classification: Primary: 93B36, 93D15; Secondary: 46J15.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    J. Ball and A. SasaneExtension of the $\nu$-metric, preprint, arXiv:1003.0108.

    [2]

    J. Ball and A. SasaneExtension of the $\nu$-metric: The $H^\infty$ case, preprint, arXiv:1010.1843.

    [3]

    T. tom Dieck, "Algebraic Topology," EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2008.

    [4]

    R. Douglas, "Banach Algebra Techniques in Operator Theory," 2nd edition, Graduate Texts in Mathematics, 179, Springer-Verlag, New York, 1998.

    [5]

    J. Garnett, "Bounded Analytic Functions," revised 1st edition, Graduate Texts in Mathematics, 236, Springer, New York, 2007.

    [6]

    Y. Inouye, Parametrization of compensators for linear systems with transfer functions of bounded type, Technical Report 88-01, Faculty of Eng. Sci., Osaka University, Osaka, Japan, March 1988.

    [7]

    K. Mikkola, Weakly coprime factorization and state-feedback stabilization of discrete-time systems, Mathematics of Control, Signals, and Systems, 20 (2008), 321-350.doi: 10.1007/s00498-008-0034-z.

    [8]

    N. Nikolski, "Treatise on the Shift Operator. Spectral Function Theory," Grundlehren der Mathematischen Wissenschaften, 273, Springer-Verlag, Berlin, 1986.

    [9]

    N. Nikolski, "Operators, Functions, and Systems: An Easy Reading. Vol. 1. Hardy, Hankel, and Toeplitz," Mathematical Surveys and Monographs, 92, American Mathematical Society, Providence, RI, 2002.

    [10]

    W. Rudin, "Functional Analysis," 2nd edition, International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991.

    [11]

    D. Sarason, Toeplitz operators with piecewise quasicontinuous symbols, Indiana University Mathematics Journal, 26 (1977), 817-838.doi: 10.1512/iumj.1977.26.26066.

    [12]

    M. Smith, On stabilization and the existence of coprime factorizations, in "Realization and Modelling in System Theory" (Amsterdam, 1989), Progr. Systems Control Theory, 3, Birkhäuser Boston, Boston, MA, (1990), 215-222.

    [13]

    G. Vinnicombe, Frequency domain uncertainty and the graph topology, IEEE Transactions on Automatic Control, 38 (1993), 1371-1383.doi: 10.1109/9.237648.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(70) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return