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

作者：Hara Tadayuki^*; Sakata Sadahisa

来源：Applied Mathematics Letters, 2011, 24(1): 12-15.

DOI：10.1016/j.aml.2010.07.015

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

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.

• 出版日期2011-1