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General dynamical systems and conditional stability

Published online by Cambridge University Press:  24 October 2008

A. A. Kayande  and
V. Lakshmikantham
A. A. Kayande
Affiliation:
Marathwada University, India and University of Alberta, Canada
V. Lakshmikantham
Affiliation:
Marathwada University, India and University of Alberta, Canada
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Extract

The notion of a general dynamical system was introduced by Barbashin(1). In this paper we consider a general dynamical system in a metric space following Zubov(6) where Lyapunov's method has been extended to investigate the stability properties using a single Lyapunov functional.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 199 - 207
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Barbasin, E. A.On the Theory of generalised dynamical systems. Učen. Zap. M.G.U no. 135, pp. 110–133 (1949), (Russian).Google Scholar
(2)Lakshmikantham, V.Differential Systems and Extension of Lyapunov Method. Michigan. Math. J. 9 (1962), 311–320.CrossRefGoogle Scholar
(3)Lakshmikantham, V.Differential equations in Banach spaces and extension of Lyapunov method. Proc. Cambridge Philos. Soc. 59 (1963), 509–513.CrossRefGoogle Scholar
(4)Laxshmikantham, V.Vector Lyapunov functions and conditional stability. J. Math. Anal. Appl. 10 (1965), 368–377.CrossRefGoogle Scholar
(5)Wazèewski, T.Systèmes des équations et des inequalités différentiellea ordinaires aus déuxièmes membres monotones et leurs applications. Ann. Polon. Math. 23 (1950), 112–166.Google Scholar
(6)Zubov, V. I. Methods of A. M. Lyapunov and their application. AEC–tr–4439 (1961). Original: Metody Liapunova i ikh primenenie. Izdat. Leningrad University, (1957).Google Scholar