Multiplicity and Stable Varieties of Time-delay Systems : A Missing Link

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Multiplicity-induced-dominancy for delay-differential equations of retarded type (2020, methodology): “1) by exploiting the integral factorization introduced in [9].”
Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system (2017, background): “(4) In [13], it is shown that for a given delay τ ∈ R+, equation (4) admits a double spectral value at z = z0 if and only if z0 = −a0τ + 1/τ and a1 = e−a0τ−1/τ.”
Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design (2020, unknown): “It was shown in [15] that for a given positive delay, equation (3.1) admits a double spectral value at s = s 0 if, and only if, In addition, it was emphasized that s 0 is the rightmost root, and that if s 0 < 0 then the zero solution of system (3.1) is asymptotically stable; see [16] for general…”
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”