On the Roots of Characteristic Equations of Delay Differential Systems

TL;DR

This paper demonstrates that certain delay differential systems can have infinitely many complex roots in their characteristic equations, under mild coefficient conditions, impacting the understanding of their stability properties.

Contribution

It establishes the existence of infinitely many roots for characteristic equations of delay differential systems under specific mild conditions, a novel theoretical insight.

Findings

Characteristic equations can have infinitely many roots.

Roots can be complex and unbounded.

Implications for stability analysis of delay systems.

Abstract

We prove that characteristic equations of certain types of delay differential systems, under some mild conditions on their coefficients, can possess infinitely many complex roots.