A test for stability of linear differential delay equations
Author:
J. M. Mahaffy
Journal:
Quart. Appl. Math. 40 (1982), 193-202
MSC:
Primary 34K20
DOI:
https://doi.org/10.1090/qam/666674
MathSciNet review:
666674
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Abstract: The changes in the stability of a system of linear differential delay equations resulting from the delay are studied by analyzing the associated eigenvalues of the characteristic equation. A specific contour is mapped by the characteristic equation into the complex plane to give an easy test for stability from an application of the argument principle. When the real part of an eigenvalue is positive, the contour gives bounds on the imaginary part which are important in certain applications to nonlinear problems.
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K. Ogata, Modern control engineering, Prentice-Hall, Inc., Englewood, Cliffs, N. J., 1970
R. Bellman and K. Cooke, Differential-difference equations, Academic Press, New York, 1963
R. Churchill, J. Brown and R. Verhey, Complex variables and applications, McGraw-Hill, New York, 1976
J. K. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977
P. Lancaster, Theory of matrices, Academic Press, New York, 1969
J. M. Mahaffy, Periodic solutions for certain protein synthesis models, J. Math. Anal. Appl. 74, 72–105, (1980).
R. D. Nussbaum, Periodic solutions of some nonlinear autonomous functional differential equations, Ann. Mat. Pura. Appl. Ser. 4, 51, 263–306 (1974)
K. Ogata, Modern control engineering, Prentice-Hall, Inc., Englewood, Cliffs, N. J., 1970
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Article copyright:
© Copyright 1982
American Mathematical Society
