Insights into the multiplicity-induced-dominancy for scalar delay-differential equations with two delays
Abstract
It has been observed in recent works that, for several classes of linear time-invariant time-delay systems of retarded or neutral type with a single delay, if a root of its characteristic equation attains its maximal multiplicity, then this root is the rightmost spectral value, and hence it determines the exponential behavior of the system, a property usually referred to as multiplicity-induced-dominancy (MID). In this paper, we investigate the MID property for one of the simplest cases of systems with two delays, a scalar delay-differential equation of first order with two delayed terms of order zero. We discuss the standard approach based on the argument principle for establishing the MID property for single-delay systems and some of its limitations in the case of our simple system with two delays, before proposing a technique based on crossing imaginary roots that allows to conclude that the MID property holds in our setting.
Keywords
Cite
@article{arxiv.2107.11348,
title = {Insights into the multiplicity-induced-dominancy for scalar delay-differential equations with two delays},
author = {Sébastien Fueyo and Guilherme Mazanti and Islam Boussaada and Yacine Chitour and Silviu-Iulian Niculescu},
journal= {arXiv preprint arXiv:2107.11348},
year = {2021}
}
Comments
16th IFAC Workshop on Time Delay Systems (IFAC TDS 2021)