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IMA Journal of Mathematical Control and Information Advance Access originally published online on October 21, 2005
IMA Journal of Mathematical Control and Information 2006 23(3):259-268; doi:10.1093/imamci/dni057
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Pham Huu Anh Ngoc1,** and Byung-Soo Lee2

1 Department of Mathematics, Hue University, 32 Le Loi Street, Hue City, Vietnam, 2 Department of Mathematics, KyungSung University, Busan 608-736, Korea

** Email: phanhngoc{at}yahoo.com

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.

Received on 16 September 2004. accepted on 3 March 2005.


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