Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] J. A. Yorke, Asymptotic properties of solutions using the second derivative of a Liapunov function, Ph.D. Dissertation, University of Maryland, College Park.
  • [2] M. B. Kudaev, A study of the behavior of the trajectories of systems of differential equations by means of Lyapunov functions, Dokl. Akad. Nauk. SSSR 147 (1962), 1285-1287 =Soviet Math. Dokl. 3 (1962), 1802-1804. MR 26 #1586. MR 0144038 (26:1586)
  • [3] A. R. Butz, Higher order derivatives of Liapunov functions, IEEE Trans. Automatic Control AC14 (1969), 111-112. MR 0251315 (40:4546)
  • [4] J. Szarski, Differential inequalities, Monografie Mat., Tom 43, PWN, Warsaw, 1965. MR 32 #7822. MR 0190409 (32:7822)
  • [5] T. Yoshizawa, Stability theory by Liapunov's second method, Publ. Math. Soc. Japan, no. 9, Math. Soc. Japan, Tokyo, 1966. MR 34 #7896. MR 0208086 (34:7896)
  • [6] V. Lakshmikantham and S. Leela, Differential and integral inequalities. Vol. I. Academic Press, New York, 1969.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34.40

Retrieve articles in all journals with MSC: 34.40


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

American Mathematical Society