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

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