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A Short Note on Stability of Linear Time Delay Systems

[+] Author Affiliations
M. S. Medenica

Polytechnic Academy, New Belgrade, Serbia

D. Lj. Debeljkovic

University of Belgrade, Belgrade, Serbia

Paper No. ESDA2006-95055, pp. 19-23; 5 pages
doi:10.1115/ESDA2006-95055
From:
  • ASME 8th Biennial Conference on Engineering Systems Design and Analysis
  • Volume 3: Dynamic Systems and Controls, Symposium on Design and Analysis of Advanced Structures, and Tribology
  • Torino, Italy, July 4–7, 2006
  • ISBN: 0-7918-4250-9 | eISBN: 0-7918-3779-3
  • Copyright © 2006 by ASME

abstract

Our research on stability criteria for linear systems with time delay in a frequency domain has brought in a new stability criterion that belongs to the group of graph-analytical stability criteria. Via the theory of functions with a complex variable, this criterion is based upon Cauchy’s theorem of argument and condition that for frequency ω varying from −∞ to +∞ the argument of function f*(jω,ejωτ ) has positive change. In solution, as a graphic interpretation in the f* - plane, a spiral curve is obtained, which possesses some characteristics crucial for the stability of a system with time delay. Through given examples, simplicity and facility of criteria application to different cases of systems are shown.

Copyright © 2006 by ASME
Topics: Stability , Delays

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