• DocumentCode
    21617
  • Title

    Zero Crossings, Overshoot and Initial Undershoot in the Step and Impulse Responses of Linear Systems

  • Author

    Damm, Tobias ; Muhirwa, Luc N.

  • Author_Institution
    Dept. of Math., Univ. of Kaiserslautern, Kaiserslautern, Germany
  • Volume
    59
  • Issue
    7
  • fYear
    2014
  • fDate
    Jul-14
  • Firstpage
    1925
  • Lastpage
    1929
  • Abstract
    We consider functions in the time and the frequency domain, and show how the occurrence of real zeros in the frequency domain is related to the number of zero crossings, overshoot and initial undershoot in the time domain. This leads to simple proofs of known facts for linear time-invariant systems and their generalizations in various directions. In particular, we consider time-delay systems and differential systems of fractional order.
  • Keywords
    delays; frequency-domain analysis; linear systems; time-domain analysis; transient response; fractional order differential systems; frequency domain; impulse response; initial undershoot; linear time-invariant systems; overshoot; time domain; time-delay systems; zero crossings; Delays; Frequency-domain analysis; Laplace equations; Linear systems; Polynomials; Transfer functions; Linear system; polynomials;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.2013.2294616
  • Filename
    6681959