Annali di Matematica Pura ed Applicata

, Volume 78, Issue 1, pp 91–103 | Cite as

On the stability properties of a third order system

  • G. P. Szegö
  • C. Olech
  • A. Cellina


A third order differential equation suggested by a problem in power system is considered.

The combined application of very general results, namely the topological method of Wazewski[1,3], the extension theorem[1,5] and the topological properties of attractors[1,9] leads to a complete qualiiative description of the behaviour of the solutions of the equation.


Differential Equation Power System General Result Stability Property Topological Property 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    N. P. Bhatia andG. P. Szegö,Dynamical systems: Stability Theory and Applications, Lecture Notes in Mathematics N. 35 Springer Verlag, New York-Heidelberg-Berlin.Google Scholar
  2. [2]
    A. M. Liapunov,Problème géneral de la stabilité du mouvement, Kharkov, 1892, French Translation, Ann. Math. St. N. 17, Princeton University Press, Princeton 1947.Google Scholar
  3. [3]
    T. Wazewski,Sur un principe topologique de l’examen de l’allure asymqtotique des intégrales des équations différentielles ordinaires, Ann. Soc. Polon. Math. vol. 20 (1947) pp. 279–313.MathSciNetGoogle Scholar
  4. [4]
    A. Pliś,Sets filled by asymptotic integrals of ordinary differential equations, Bull. Acad. Pol. Sc. Cl. III, vol. 4, (1956), pp. 749–752.Google Scholar
  5. [5]
    N. P. Bhatia andG. P. Szegö,An extension theorem for asymptotic stability, Proc. Internat. Symposium on Diff. Equations and Dynamical System. Portorico 1966, Academic Press. New York 1967.Google Scholar
  6. [6]
    E. A. Barbashin andN. N. Krasovskii,On the stability of motion in the large, Pokl. Acad. Nauk SSSR, vol. 86 (1952), pp. 453–456.Google Scholar
  7. [7]
    J. P. La Salle,An invariance principle in the theory of stability, Brown University, Center for Dynamical Systems, Tech. Rept. 66-I.Google Scholar
  8. [8]
    —— ——,The extent of asymptotic stability, Proc. Nat. Acad. Sc. vol. 46 (1960), pp. 363–365.zbMATHGoogle Scholar
  9. [9]
    N. P. Bhatia andG. P. Szegö,Weak attractors in R n, Math. System Theory, vol. 1, (1967), pp. 129–134.CrossRefMathSciNetGoogle Scholar
  10. [10]
    P. Hartman,Ordinary Differential Equations, J. Wiley, New York, 1964.Google Scholar
  11. [11]
    M. W. Siddiqee,Direct method of Liapunov and transient stability analysis, Ph. D. Thesis, Univ. Minnesota, Minneapolis, Aug. 1967.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1968

Authors and Affiliations

  • G. P. Szegö
    • 1
  • C. Olech
    • 2
  • A. Cellina
    • 1
  1. 1.Università di MilanoMilanoItaly
  2. 2.Institut Matematiki, PANKrakowPoland

Personalised recommendations