On a functional equation arising in the stability theory of difference-differential equations
Authors:
W. B. Castelan and E. F. Infante
Journal:
Quart. Appl. Math. 35 (1977), 311-319
MSC:
Primary 34K05
DOI:
https://doi.org/10.1090/qam/492694
MathSciNet review:
492694
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Abstract: The functional differential equation \[ Q’\left ( t \right ) = AQ\left ( t \right ) + B{Q^T}\left ( {\tau - t} \right ), - \infty < t < \infty \], where $A$, $B$ are $n \times n$ constant matrices, $\tau \ge 0$, $Q\left ( t \right )$ is a differentiable $n \times n$ matrix and ${Q^T}\left ( t \right )$ is its transpose, is studied. Existence, uniqueness and an algebraic representation of its solutions are given.
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E. F. Infante and W. B. Castelan, A Liapunov functional for a matrix differential difference equation, to appear
E. F. Infante and J. A. Walker, A Liapunov functional for a scalar differential difference equation, Proc. Roy. Soc. Edinburgh (to appear)
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R. Bellman, Introduction to matrix theory, McGraw Hill, 1960
R. Bellman, and K. Cooke, Differential difference equations, Academic Press, 1963
E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955
R. Datko, An algorithm for computing Liapunov functionals for some differential difference equations, in Ordinary differential equations, 1971 NRL-MRC Conference, Academic Press, 1972, p. 387–398
J. K. Hale, Ordinary differential equations, Wiley-Interscience, 1969
J. K. Hale, Functional differential equations, Appl. Math. Science Series, Springer-Verlag, 1971
J. K. Hale, Theory of functional differential equations, Appl. Math. Science Series, Springer-Verlag, 1977
E. F. Infante and W. B. Castelan, A Liapunov functional for a matrix differential difference equation, to appear
E. F. Infante and J. A. Walker, A Liapunov functional for a scalar differential difference equation, Proc. Roy. Soc. Edinburgh (to appear)
P. Lancaster, Theory of matrices, Academic Press, 1969
I. M. Repin, Quadratic Liapunov functionals for systems with delays, Prikl. Math. Mech. 29, 564–566 (1965)
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Article copyright:
© Copyright 1977
American Mathematical Society
