• DocumentCode
    1362481
  • Title

    Gramian assignment based on the Lyapunov equation

  • Author

    Wicks, Mark A. ; DeCarlo, Raymond A.

  • Author_Institution
    Sch. of Electr. Eng., Purdue Univ., West Lafayette, IN, USA
  • Volume
    35
  • Issue
    4
  • fYear
    1990
  • fDate
    4/1/1990 12:00:00 AM
  • Firstpage
    465
  • Lastpage
    468
  • Abstract
    A theorem on the assignability of the controllability Gramian using state feedback is presented. The approach is based on the Lyapunov equation. Specifically, it shows that the set of Gramian matrices which are assignable using state feedback lies in a vector space and is precisely the intersection of that vector space with the set of positive definite matrices. The results show that it may be possible to reshape the structure of the system indirectly by specifying a desired closed-loop Lyapunov function, rather than by directly assigning eigenvalues or eigenvectors
  • Keywords
    Lyapunov methods; closed loop systems; control system analysis; controllability; eigenvalues and eigenfunctions; feedback; state-space methods; Lyapunov equation; assignability; closed-loop; controllability; eigenvalues; eigenvectors; gramian assignment; state feedback; vector space; Controllability; Covariance matrix; Eigenvalues and eigenfunctions; Ellipsoids; Energy dissipation; Equations; Lyapunov method; State feedback; Stochastic systems; Vectors;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/9.52304
  • Filename
    52304