Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Stability conditions for linear nonautonomous delay differential equations


Authors: Stavros N. Busenberg and Kenneth L. Cooke
Journal: Quart. Appl. Math. 42 (1984), 295-306
MSC: Primary 34K20
DOI: https://doi.org/10.1090/qam/757167
MathSciNet review: 757167
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Abstract: We derive new sufficient conditions for uniform asymptotic stability of the zero solution of linear non-autonomous delay differential equations. The equations considered include scalar equations of the form

$\displaystyle x'\left( t \right) = - c\left( t \right)x\left( t \right) + \sum\limits_{i = 1}^n {{b_i}\left( t \right)x\left( {t - {T_i}} \right)} $

where $ c\left( t \right)$, $ {b_i}\left( t \right)$ are continuous for $ t \ge 0$ and $ {T_i}$ is a positive number $ (i = 1, 2,...,n)$, and also systems of the form

$\displaystyle x'(t) = B(t)x(t - T) - C(t)x(t)$

where $ B(t)$) and $ C(t)$ are $ n \times n$ matrices. The results are found by using the method of Lyapunov functionals.

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DOI: https://doi.org/10.1090/qam/757167
Article copyright: © Copyright 1984 American Mathematical Society


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