An application of the Hurwitz theorem to the root analysis of the characteristic equation

被引：5

作者：

Hara, Tadayuki ^{[1
]}

Sakata, Sadahisa ^{[2
]}

机构：

[1] Osaka Prefecture Univ, Dept Math Sci, Osaka 5998531, Japan

[2] Osaka Electrocommun Univ, Res Ctr Phys & Math, Osaka 5728530, Japan

来源：

APPLIED MATHEMATICS LETTERS | 2011年 / 24卷 / 01期

关键词：

Asymptotic stability; Integro-differential equation; Root analysis; Characteristic equation; Delay;

D O I：

10.1016/j.aml.2010.07.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we show that a classical result of A. Hurwitz is still very effective in studying the root analysis of the characteristic equation for a linear functional differential equation. A conjecture was made by Funakubo et al. (2006) [3] regarding the asymptotic stability condition of the zero solution of a linear integro-differential equation of Volterra type. We applied the Hurwitz theorem to the characteristic equation in question and showed the existence of a root with positive real part and solved the conjecture. The Hurwitz theorem is expected to work well for the root analysis in critical cases. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：12 / 15

页数：4