Advertisement

Ingenieur-Archiv

, Volume 35, Issue 5, pp 332–339 | Cite as

Stability indicative function and its application to systems with time delay

  • Yasutada Kashiwagi
  • I. Flügge-Lotz
Article

Summary

For investigating stability of linear systems with time delay, it is not sufficient to know critical values of such a parameter as time delay. In order to determine whether or not the system is stable for a given delay, the “stability indicative function” is introduced. This function is applied to second- and third-order linear systems with time delay and the stability regions of several cases are obtained. Some examples clearly show that the existence of time delay may make a stable system unstable or an unstable system stable. This phenomenon is explained from a theoretical point of view.

Keywords

Neural Network Time Delay Linear System Complex System Information Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Übersicht

Die Ermittlung kritischer Totzeitwerte ist nicht ausreichend für Stabilitätsuntersuchungen von linearen Systemen mit Totzeiten, die durch Differential-Differenzen-Gleichungen beschrieben werden. Um festzustellen, ob ein System mit vorgegebener Totzeit stabil ist, kann man eine „stabilitätsbestimmende Funktion” einführen und untersuchen. Diese Funktion wird benutzt, um lineare Systeme zweiter und dritter Ordnung zu studieren und die Stabilitätsgebiete für verschiedene Fälle zu bestimmen. Beispiele zeigen, daß das Auftreten von Totzeiten stabile Systeme unstabil machen kann und umgekehrt unstabile Systeme stabilisieren kann.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. A. Sokolov, The Stability Criterion in Linear Systems With Distributed Parameters and its Application, Inžen. Sb., Vol. 2, No. 2, 1946 (Received 1940).Google Scholar
  2. [2]
    E. P. Popov, The Dynamics of Automatic Control Systems, Massachusetts: Addison-Wesley Publ. 1962, Chap. XII.Google Scholar
  3. [3]
    Y. Kashiwagi and I. Flügge-Lotz, Stability of Linear Systems with Time Delay, Internal Technical Report No. 156, Engineering Mechanics, Stanford University, 1965.Google Scholar
  4. [4]
    H. I. Ansoff and J. A. Krumhansl, Quart. Appl. Math. 6 (1948) p. 337.Google Scholar
  5. [5]
    N. N. Krasovskii, Stability of Motion, Stanford: Stanford University Press 1963.Google Scholar
  6. [6]
    L. S. Pontryagin, Izv. Akad. Nauk SSSR. Ser. Mat. 6 (1942) p. 115; Amer. Math. Soc. Transl. 2 (1955) p. 95.Google Scholar
  7. [7]
    S. J. Bhatt and C. S. Hsu, J. Appl. Mech., Paper No. 65 — APMW — 11, 1965.Google Scholar
  8. [8]
    R. Bellman and K. L. Cooke, Differential-Difference Equations, New York, 1963.Google Scholar

Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • Yasutada Kashiwagi
    • 1
  • I. Flügge-Lotz
    • 2
  1. 1.Virginia Polytechnic InstituteBlacksburg
  2. 2.Stanford UniversityStanfordUSA

Personalised recommendations