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1 results

  • 15 - Constrained Interpolation

  • from Part II - Further Contributions to Matrix Theory
  • Patrick Dewilde, Technische Universität München, Klaus Diepold, Technische Universität München, Alle-Jan Van der Veen, Technische Universiteit Delft, The Netherlands
  • Book:
    Time-Variant and Quasi-separable Systems
    Published online:
    24 October 2024
    Print publication:
    31 October 2024, pp 242-253

  • Summary

    The chapter shows how classical interpolation problems of various types (Schur, Nevanlinna–Pick, Hermite–Fejer) carry over and generalize to the time-variant and/or matrix situation. We show that they all reduce to a single generalized constrained interpolation problem, elegantly solved by time-variant scattering theory. An essential ingredient is the definition of the notion of valuation for time-variant systems, thereby generalizing the notion of valuation in the complex plane provided by the classical z-transform.