On the MID Property in Planar Delay Systems. Towards a Partial Pole Placement in the Multidimensional case

In recent works, a new stabilization paradigm called Partial Pole Placement has been set for single-delay single-input single-output systems of linear time-invariant delay differential equations. In fact, the PPP has the advantage of prescribing the closed-loop exponential decay rate since it consists in assigning the corresponding rightmost spectral value thanks to two remarkable spectral properties called respectively multiplicity-induced-dominancy (MID) and coexistant-real-roots inducing multiplicity (CRRID). In this note, we show the validity of the MID property in planar delay systems when some spectral value achieves its maximal multiplicity, thus opening new perspectives in the prescribed stabilization for delay systems with commensurate delays.