A procedure for determination of the exponential stability of certain differential-difference equations
Author:
R. Datko
Journal:
Quart. Appl. Math. 36 (1978), 279-292
MSC:
Primary 34K20
DOI:
https://doi.org/10.1090/qam/508772
MathSciNet review:
508772
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Abstract: Certain continuity properties of the spectra of linear autonomous differential-difference equations which depend on a parameter are developed. These results are used to obtain a practical criterion for determination of the exponential stability of these systems.
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S. Saks and A. Zygmund, Analytic functions, Elsevier Publishing Co., New York, 1971
A. S. Besicovitch, Almost periodic functions, Dover Publications. Inc., 1954
H. Bohr, Collected Mathematical Works, Vol. 1, Dansk Matemetisk Forening, KØbenhavn, 1952. See also H. Bohr, Über die gleich Mässige Konvergenz Dirichletsher Reihen, J. Reine Angew. Math. 143, 203–211 (1913)
R. Datko, Representation and stability of linear differential-difference equations in a Banach space, to appear.
R. Datko, The stabilization of linear functional differential equations, in Calculus of variations and control theory, ed. D. L. Russell, Academic Press, Inc., New York, 1975, pp. 353–369
L. E. El’sgol’ts and S. B. Norkin, Introduction to the theory and application of differential equations with deviating arguments, Academic Press, New York, 1973
J. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977
D. Henry, Linear autonomous neutral functional differential equations, J. Diff. Eqs. 15, 106–128 (1974)
S. Saks and A. Zygmund, Analytic functions, Elsevier Publishing Co., New York, 1971
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Article copyright:
© Copyright 1978
American Mathematical Society
