Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system

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Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design (2020, unknown): “By exploiting the delay eﬀect, the following proposition proved in [13, 14] asserts that the solution’s decay rate can be further improved by decreasing the corresponding rightmost root.”
The generic multiplicity-induced-dominancy property from retarded to neutral delay-differential equations: When delay-systems characteristics meet the zeros of Kummer functions (2021, background): “For instance, the MID or GMID properties are shown to hold for retarded equations of order 1 in [18], which proves dominance by introducing a factorization of ∆ in terms of an integral expression when it admits a root of maximal multiplicity 2; for retarded equations of order 2 with a delayed term o”
Multiplicity-induced-dominancy for delay-differential equations of retarded type (2020, methodology): “MID has been shown to hold, for instance, in the case n = 1, proving dominance by introducing a factorization of ∆ in terms of an integral expression when it admits a root of multiplicity 2 [9]; in the case n = 2 and α1 = 0, using also the same factorization technique [8]; and in the case n = 2 and ”