• DocumentCode
    806350
  • Title

    A characterization of eAtand a constructive proof of the controllability criterion

  • Author

    Vidyasagar, M.

  • Author_Institution
    Sir George Williams University, Montreal, P. Q., Canada
  • Volume
    16
  • Issue
    4
  • fYear
    1971
  • fDate
    8/1/1971 12:00:00 AM
  • Firstpage
    370
  • Lastpage
    371
  • Abstract
    A differential equation characterizing the functions \\alpha _{i}(t) , which arise when eAtis expressed as \\alpha _{0}(t)I + ... + \\alpha _{n-1}(t) A^{n-1} , is derived. It is shown that the set of functions {\\alpha _{i}(t)} is linearly independent over any nonzero interval. Using this fact, a constructive proof is given for the well-known criterion for a linear time-invariant system to be controllable, namely, rank [B|AB| ... |A^{n-1}B] = n .
  • Keywords
    Controllability; Linear systems, time-invariant continuous-time; Matrix functions; Analog computers; Automatic control; Computational Intelligence Society; Control systems; Controllability; Differential equations; Polynomials; Sufficient conditions; Testing;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1971.1099751
  • Filename
    1099751
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=806350