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1998 Exponential asymptotic stability in linear delay-differential equations with variable coefficients
Tadayuki Hara, Yuko Matsumi, Rinko Miyazaki
Differential Integral Equations 11(2): 263-278 (1998).

Abstract

In this paper we give some new necessary and sufficient conditions under which the zero solution of the linear delay-differential equations with variable coefficients $$ x'(t)=A(t)x(t-\tau) \tag L $$ is exponentially asymptotically stable. For example, in the case $$ A(t) = -\rho(t)\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}, $$ where $\rho(t) > 0,$ $\lim_{t \to \infty} \int_{t-\tau}^t \rho(s)\,ds = q>0$ and $|\theta| < \frac{\pi}{2},$ the zero solution of (L) is exponentially asymptotically stable if and only if $ q <\frac{\pi}{2}-|\theta|$.

Citation

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Tadayuki Hara. Yuko Matsumi. Rinko Miyazaki. "Exponential asymptotic stability in linear delay-differential equations with variable coefficients." Differential Integral Equations 11 (2) 263 - 278, 1998.

Information

Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1017.34076
MathSciNet: MR1741845

Subjects:
Primary: 34K20

Rights: Copyright © 1998 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.11 • No. 2 • 1998
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