Effects of Roots of Maximal Multiplicity on the Stability of Some Classes of Delay Differential-Algebraic Systems: The Lossless Propagation Case

Abstract

It has been observed in several recent works that, for some classes of linear time-delay systems, spectral values of maximal multiplicity are dominant, a property known as multiplicity-induced-dominancy (MID). This paper starts the investigation of whether MID holds for delay differential-algebraic systems by considering a single-delay system composed of two scalar equations. After motivating this problem and recalling some recent results for retarded delay differential equations, we prove that the MID property holds for the delay differential-algebraic system of interest and present some applications.

24th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2020), Cambridge, UK, 23-27 August 2021

References in corpus (1)

• Multiplicity-induced-dominancy for delay-differential equations of retarded type

Cited by in corpus (3)

• The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: When delay-systems characteristics meet the zeros of Kummer functions
• New Features of P3$\delta$ software: Partial Pole Placement via Delay Action
• Insights into the multiplicity-induced-dominancy for scalar delay-differential equations with two delays