Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T08:32:53.040Z Has data issue: false hasContentIssue false
  • English
  • Français

A star-shaped condition for stability of linear retarded functional differential equations†

Published online by Cambridge University Press:  14 November 2011

Richard Silkowski
Richard Silkowski
Affiliation:
IBM Corporation, Poughkeepsie, New York 12602, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

Sufficient conditions are developed for asymptotic stability of the autonomous linear functional differential equation of retarded type. If the asymptotic stability of

implies the asymptotic stability of

then these conditions are also necessary. Necessary and sufficient conditions are developed for the largest cone in the region of stability. These results are illustrated with the example

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 3-4 , 1979 , pp. 189 - 198
Copyright
Copyright © Royal Society of Edinburgh 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bellman, R. and Cooke, K.. Differential-Difference Equations (New York: Academic Press, 1963).Google Scholar
2Hale, J.. Functional Differential Equations. Appl. Math. Sci. 3 (New York: Springer-Verlag, 1977).Google Scholar
3Hayes, N. D.. Roots of the Transcendental Equation Associated with a Certain Difference-Differential Equation. J. London Math. Soc. 25 (1950), 226–232.Google Scholar
4Noonburg, V. W.. roots of a transcendental equation associated with a system of differential-difference equations. SIAM J. Appl. Math. 17 (1969), 198–205.CrossRefGoogle Scholar
5Pontryagin, L. S.. On the zeros of some elementary transcendental functions. Amer. Math. Soc. Transi 1 (1955), 95–110.Google Scholar
6Zivotovskii, L. A.. Absolute stability for the solutions of differential equations with retarded arguments. Trudy Sem. Teor. Differencial. Uravneniῐ s Otklon. Argumentom 7 (1969), 82–91.Google Scholar