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

✍ Scribed by Tadayuki Hara; Sadahisa Sakata

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 218 KB
• Volume: 24
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2010.07.015

✦ Synopsis

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 [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.