The MID property for a second-order neutral time-delay differential equation

International audienceThis paper considers the Multiplici- ty-Induced-Dominancy (MID) property for second order neutral time-delay differential equations. Necessary and sufficient conditions for the exis- tence of a root of maximal multiplicity are given in terms of this root and the parameters (includ- ing the delay) of the given equation. Links with dominancy of this root and with the exponential stability property of the solution of the consid- ered equations are given. Finally, we illustrate the obtained results on the classical oscillator control problem