• DocumentCode
    1217677
  • Title

    The largest singular value of eXA0e -X is convex on convex sets of commuting matrices

  • Author

    Sezginer, Renan Sezer ; Overton, Michael L.

  • Author_Institution
    Courant Inst. of Math. Sci., New York Univ., NY, USA
  • Volume
    35
  • Issue
    2
  • fYear
    1990
  • fDate
    2/1/1990 12:00:00 AM
  • Firstpage
    229
  • Lastpage
    230
  • Abstract
    A short and direct proof of the convexity property is given. It is shown that the theorem applies to any convex, commuting set of matrices in RnXn, where A0∈RnXn is fixed. It is also shown that the result does not hold if X is permitted to be a general square matrix. A counterexample is supplied for noncommuting matrices
  • Keywords
    matrix algebra; optimisation; commuting matrices; convex sets; convexity property; general square matrix; largest singular value; matrix algebra; noncommuting matrices; optimisation; Adaptive control; Asymptotic stability; Automatic control; Differential equations; Feedback amplifiers; Gaussian processes; Network synthesis; Programmable control; Robust control; Uncertainty;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/9.45196
  • Filename
    45196
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1217677