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5.—The Uniform Asymptotic Stability of Certain Linear Differential-difference Equations

Published online by Cambridge University Press:  14 February 2012

R. Datko
Affiliation:
Georgetown University, Washington, DC 20007, USA

Synopsis

A necessary and sufficient condition is developed for determination of the uniform stability of a class of non-autonomous linear differential-difference equations. This condition is the analogue of the Liapunov criterion for linear ordinary differential equations.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

1Bellman, R. and Cooke, K. L.. Differential-difference equations (NewYork: Academic Press, 1963).Google Scholar
2Datko, R.. Uniform asymptotic stability of evolutionary processes in a Banach space. SIAM J. Math. Anal. 3 (1972), 428445.CrossRefGoogle Scholar
3Datko, R.. An algorithm for computing Liapunov functional for some differential-difference equations. In Ordinary differential equations, Weiss, L., Ed. (New York: Academic Press, 1972).Google Scholar
4Driver, R. D.. Existence and stability of solutions of a delay-differential system. Arch. Rational Mech. Anal. 19 (1962), 401426.CrossRefGoogle Scholar
5Dunford, N. and Schwarz, J. T.. Linear operators, 1 (New York: Wiley, 1958).Google Scholar
6Hahn, W.. Theory and application of Liapunov's direct method(Englewood Cliffs: Prentice-Hall, 1963.Google Scholar
7Hale, J.. Functional differential equations (New York: Springer Verlag, 1971).CrossRefGoogle Scholar
8Krupnova, N. I. and Shimanov, S. N.. Criterion of stability of linear systems with variable coefficients and time lag. J. appl. Math. Mech. 36 (1972), 502506. (English translation of Prikl. Mat. Meh. 36 (1972), 533–635).CrossRefGoogle Scholar