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Stability indicative function and its application to systems with time delay

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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.

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.

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References

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Author notes

  1. Yasutada Kashiwagi (Assistant Professor of Aerospace Engineering)

    Present address: Virginia Polytechnic Institute, Blacksburg, Virginia

  2. I. Flügge-Lotz (Professor of Engineering Mechanics)

    Present address: Stanford University, Stanford, California, USA

Authors and Affiliations

    Authors
    1. Yasutada Kashiwagi
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    2. I. Flügge-Lotz
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    Additional information

    This research was supported by the Air Force Office of Scientific Research, Office of Aerospace Research, under Contract AF 49 (638) 1431.

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    Kashiwagi, Y., Flügge-Lotz, I. Stability indicative function and its application to systems with time delay. Ing. arch 35, 332–339 (1967). https://doi.org/10.1007/BF00535255

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    • DOI: https://doi.org/10.1007/BF00535255

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