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Proceedings of the American Mathematical Society

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A comparision lemma for higher order trajectory derivatives


Author: R. W. Gunderson
Journal: Proc. Amer. Math. Soc. 27 (1971), 543-548
MSC: Primary 34.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0273104-6
MathSciNet review: 0273104
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Abstract: A basic result from higher order differential inequalities is used to obtain a comparison lemma, useful when higher order trajectory derivatives of Liapunov functions are known.


References [Enhancements On Off] (What's this?)

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  • [2] M. B. Kudaev, A study of the behaviour of the trajectories of systems of differential equations by means of Lyapunov functions, Dokl. Akad. Nauk SSSR 147 (1962), 1285–1287 (Russian). MR 0144038
  • [3] Arthur R. Butz, Higher order derivatives of Liapunov functions, IEEE Trans. Automatic Control AC-14 (1969), 111–112. MR 0251315
  • [4] Jacek Szarski, Differential inequalities, Monografie Matematyczne, Tom 43, Państwowe Wydawnictwo Naukowe, Warsaw, 1965. MR 0190409
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  • [6] V. Lakshmikantham and S. Leela, Differential and integral inequalities. Vol. I. Academic Press, New York, 1969.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0273104-6
Keywords: High order trajectory derivatives, vector $ v$-functions, comparison lemma, stability properties
Article copyright: © Copyright 1971 American Mathematical Society