Further Insights on the Partial Pole Placement in Delay Systems: Simultaneity of the MID and CRRID properties
Résumé
In recent work, the multiplicity-induced-dominancy (MID) property for single delay time-delay systems has been fully characterized in the over-order case, that is when the multiplicity of the spectral abscissa exceeds the system's order. In this note, despite the fact that this assumption is not met, we provide an analytical proof for the MID. The coexistence of real spectral values is the main ingredient. The obtained result is illustrated through the stabilization of an unstable second-order plant by a delayed PD controller.
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