Effects of Roots of Maximal Multiplicity on the Stability of Some Classes of Delay Differential-Algebraic Systems: The Lossless Propagation Case⁎G.M., I.B., and S.I.N. are also with Inria, DISCO Team, Saclay – Ile-de-France research center. Issue 9 (2021) - Mazanti, Guilherme; Boussaada, Islam; Niculescu, Silviu-Iulian; Chitour, Yacine
Abstract: It has been shown 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.