Meccanica

, Volume 11, Issue 1, pp 3–10 | Cite as

Estimating the domain of attraction of a stable equilibrium state for certain delayed differential systems of order two

  • Wiktor Baran
  • Tullio Trombetti
Article
  • 27 Downloads

Summary

We discuss the influence exerted on the stability of an equilibrium state of a second order differential-difference system by the delays existing in the coupling terms of the two system equations. On certain hypotheses an asymptotic stability condition is determined which is independent of the magnitude of delays but dependent on the magnitude of coupling. A simple method for constructing regions belonging to the domain of attraction of the considered equilibrium state is developed. Several alternative constructions and applications are discussed in detail.

Keywords

Mechanical Engineer Equilibrium State Civil Engineer Stability Condition System Equation 

Sommario

Viene discussa l'influenza che sulla stabilità ai uno stato di equilibrio di un sistema differenziale alle differenze di secondo ordine banno i ritardi incorporati nei termini di accoppiamento fra le due equazioni del sistema. Si mostra come sotto opportune ipotesi si possa determinare una condizione di stabilità asintotica che non dipende dall'entità dei ritardi, mentre dipende da quella degli accoppiamenti, e si propone un metodo semplice e flessibile per costruire regioni contenute nel dominio di attrazione dello stato di equilibrio considerato. Si discutono in dettaglio numerose costruzioni alternative ed applicazioni.

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References

  1. [1]
    N. N. Krasovskii,Stability of Motion. Stanford University Press, Stanford, California, 1963.Google Scholar
  2. [2]
    R. Driver,Existence and Stability of Solutions of a Delay — Differential System, Archives for Rational Mechanics and Analysis10, 401 (1962).Google Scholar
  3. [3]
    J. Hale,Functional Differential Equations, Springer Verlag, New York, 1971.Google Scholar
  4. [4]
    L. E. Weaver,Reactor Dynamics and Control, American Elsevier, New York, 1968.Google Scholar
  5. [5]
    E. Noldus,The Stability of Coupled — Core Nuclear Reactors, J. Engng. Math.6, 31 (1972).Google Scholar
  6. [6]
    H. S. Murray et al.,Stability of Coupled Core Reactors by the Second Method of Liapunov, J. Nucl. En. Parts A/B20, 729 (1966). See also:Google Scholar
  7. [6]a
    H. S. Murray andD. G. Schultz,Stability of Nonlinear Coupled — core Reactors, in Neutron Dynamics and Control,D. L. Heltrick andL. E. Weaver Eds., USAEC Division of Technical Information Ext., Oak Ridge, Tenn., 1966.Google Scholar
  8. [7]
    S. J. Gage et al.,Investigations on Nonlinear Stability of Coupled Nuclear Systems, in Neutron Dynamics and Control, cf. Ref. 6.Google Scholar

Copyright information

© Masson Italia Editori S.p.A 1976

Authors and Affiliations

  • Wiktor Baran
  • Tullio Trombetti
    • 1
  1. 1.Divisione FisicaCNENBolognaItaly

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