Journal Article

A characterization of spectral abscissa and Perron–Frobenius theorem of positive linear functional differential equations

Pham Huu Anh Ngoc and Byung-Soo Lee

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 23, issue 3, pages 259-268
Published in print September 2006 | ISSN: 0265-0754
Published online September 2006 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dni057
A characterization of spectral abscissa and Perron–Frobenius theorem of positive linear functional differential equations

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In this paper, we give a characterization of spectral abscissa of positive linear functional differential equations. Then the obtained result is applied to derive necessary and sufficient conditions for the exponential stability of positive linear functional differential equations. Finally, we give an extension of the classical Perron–Frobenius theorem to positive linear functional differential equations.

Keywords: Perron–Frobenius theorem; functional differential equation; positive system; stability of linear system

Journal Article.  0 words. 

Subjects: Mathematics

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