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Interpolation by Rational Matrix Functions and Stability of Feedback Systems: The 4-Block Case

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Book cover Operator Theory and Complex Analysis

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 59))

Abstract

We consider the problem of constructing rational matrix functions which satisfy a set of finite order directional interpolation conditions on the left and right, as well as a collection of infinite order directional interpolation conditions on both sides. We set down consistency requirements for solutions to exist as well as a normalization procedure to make the conditions independent, and show how the general standard problem of H ∞ control fits into this framework. We also solve an inverse problem: given an admissible set of interpolation conditions, we characterize the collection of plants for which the associated H ∞-control problem is equivalent to the prescribed interpolation problem.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball & Marek Rakowski

  2. Department of Mathematics, Southwestern Oklahoma State University, Weatherford, OK, 73096

    Joseph A. Ball & Marek Rakowski

Authors
  1. Joseph A. Ball
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  2. Marek Rakowski
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Editor information

Editors and Affiliations

  1. Research Institute for Electronic Science, Hokkaido University, Sapporo, 060, Japan

    T. Ando

  2. Raymond and Beverly Sackler Faculty of Exact Sciences School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    I. Gohberg

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© 1992 Springer Basel AG

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Ball, J.A., Rakowski, M. (1992). Interpolation by Rational Matrix Functions and Stability of Feedback Systems: The 4-Block Case. In: Ando, T., Gohberg, I. (eds) Operator Theory and Complex Analysis. Operator Theory: Advances and Applications, vol 59. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8606-2_5

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  • DOI: https://doi.org/10.1007/978-3-0348-8606-2_5

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9699-3

  • Online ISBN: 978-3-0348-8606-2

  • eBook Packages: Springer Book Archive

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