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On the stability properties of a third order system

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Summary

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.

References

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    A. M. Liapunov,Problème géneral de la stabilité du mouvement, Kharkov, 1892, French Translation, Ann. Math. St. N. 17, Princeton University Press, Princeton 1947.

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    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.

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    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.

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    —— ——,The extent of asymptotic stability, Proc. Nat. Acad. Sc. vol. 46 (1960), pp. 363–365.

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    N. P. Bhatia andG. P. Szegö,Weak attractors in R n, Math. System Theory, vol. 1, (1967), pp. 129–134.

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    M. W. Siddiqee,Direct method of Liapunov and transient stability analysis, Ph. D. Thesis, Univ. Minnesota, Minneapolis, Aug. 1967.

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Szegö, G.P., Olech, C. & Cellina, A. On the stability properties of a third order system. Annali di Matematica 78, 91–103 (1968). https://doi.org/10.1007/BF02415111

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Keywords

  • Differential Equation
  • Power System
  • General Result
  • Stability Property
  • Topological Property