Multiplicity–Induced–Dominancy property for second–order neutral differential equations with application in oscillation damping

This paper addresses the exponential stability of linear time-delay systems neutral type. In general, it is quite a challenge to establish conditions on parameters system in order guarantee such stability. Recent works emphasized link between maximal multiplicity and dominant roots. Indeed, for given multiple root be necessarily are investigated, this property known as Multiplicity-Induced-Dominancy (MID). The aim explore effect roots with admissible multiplicities exhibiting, under appropriate conditions, validity MID second-order differential equations single delay. ensuing control methodology summarized five-steps algorithm that can exploited design higher-order systems. main ingredient proposed method dominancy proof spectral values based frequency bounds established via integral equations. As an illustration, stabilization classical oscillator benefits from obtained results.