• DocumentCode
    1066267
  • Title

    Balancing transformations for unstable nonminimal linear systems

  • Author

    Therapos, Constantine P.

  • Author_Institution
    Dept. of Electr. Eng., Nat. Tech. Univ. of Athens, Greece
  • Volume
    34
  • Issue
    4
  • fYear
    1989
  • fDate
    4/1/1989 12:00:00 AM
  • Firstpage
    455
  • Lastpage
    457
  • Abstract
    It is shown that an unstable nonminimal continuous (discrete) realization (A, B, C) can be transformed via a similarity transformation into a balanced one if and only if the product of the controllability, observability Gramians is similar to a real diagonal matrix Λ. If, in addition, the eigenvalues of A , say λ, satisfy the relation λi+λ j≠0(λiλj≠1) then the matrix Λ will always be positive semidefinite, and a balanced realization with its minimal part in the internally balanced form can always be obtained
  • Keywords
    controllability; eigenvalues and eigenfunctions; linear systems; matrix algebra; observability; controllability; eigenvalues; observability; real diagonal matrix; unstable nonminimal linear systems; Control system synthesis; Controllability; Digital filters; Eigenvalues and eigenfunctions; Equations; Linear systems; Noise reduction; Observability; Reduced order systems; Yttrium;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/9.28023
  • Filename
    28023
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1066267