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

An important question of ongoing interest for linear time-delay systems is to provide conditions on its parameters guaranteeing exponential stability solutions. Recent works have explored spectral techniques show that, some low-order delay-differential equations retarded type, values maximal multiplicity are dominant, and hence determine the asymptotic behavior system, a property known as multiplicity-induced-dominancy. This work further explores such shows validity general type arbitrary order including single delay in system's representation. More precisely, an interesting link between characteristic functions with real root Kummer's confluent hypergeometric exploited. We also examples illustrating our main result.