• DocumentCode
    855952
  • Title

    An L∞error bound for the phase approximation problem

  • Author

    Li, Rongsheng ; Jonckheere, Edmond

  • Author_Institution
    University of Southern California, Los Angeles, CA, USA
  • Volume
    32
  • Issue
    6
  • fYear
    1987
  • fDate
    6/1/1987 12:00:00 AM
  • Firstpage
    517
  • Lastpage
    518
  • Abstract
    Given a random process spectral factor w(\\cdot) , the phase approximation algorithm, initiated by Jonckheere and Helton [1], constructs a reduced-order spectral factor \\hat{w}(\\cdot) such that \\parallel w/w^{\\ast }-\\hat{w}/ \\hat{w}^{\\ast }\\parallel is small in the Hankel-norm sense. In this note, we derive the L^{\\infty } error bound \\parallel w/w^{\\ast } - \\hat{w}/\\hat{w}^{\\ast }\\parallel_{\\infty } \\leq 4(\\sigma _{k+1} + ... +\\sigma _{N}) , where the σ\´s are the canonical correlation coefficients. A similar result holds in the multivariable case.
  • Keywords
    Phase estimation; Spectral factorizations; Adaptive control; Approximation algorithms; Error correction; Frequency; H infinity control; Linear approximation; Random processes; Robustness; Shape control;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1987.1104644
  • Filename
    1104644
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=855952