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Media type:
E-Article
Title:
STABILITY CONDITIONS FOR LINEAR NON-AUTONOMOUS DELAY DIFFERENTIAL EQUATIONS
Contributor:
BUSENBERG, STAVROS N.;
COOKE, KENNETH L.
imprint:
Brown University, 1984
Published in:Quarterly of Applied Mathematics
Language:
English
ISSN:
0033-569X;
1552-4485
Origination:
Footnote:
Description:
<p>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 $\[x'\left( t \right) = - c\left( t \right)x\left( t \right) + \sum\limits_{i = 1}^n {{b_i}\left( t \right)x\left( {t - {T_i}} \right)} \]$ where c(t), bi(t) are continuous for t ≥ 0 and Ti is a positive number (i=1,2,...,n), and also systems of the form x'(t) = B(t) x(t-T)-C(t) x(t) where B(t) and C(t) are n × n matrices. The results are found by using the method of Lyapunov functional.</p>