Complete stability map of neutral type first order - two time delay systems

First order linear time invariant dynamics of neutral type is taken into account with two time delays. A unique feature is included in this study, from the stability perspective: terms that add neutral dynamics into a scalar retarded type characteristic equation studied by Hale, J., et al. in 1993,. The stability posture of this new dynamics can be treated by a unique procedure, which is recently introduced for retarded type dynamics, known as cluster treatment of characteristic roots (CTCR). We show CTCR's applicability to neutral multiple delay dynamics first. Later we present several case studies to display the steps and the strengths of CTCR when applied on neutral systems. In addition, the real part of the rightmost root distribution is computed via the infinitesimal generator approach, which is recently developed for general classes of linear time delay systems. The capabilities are shown here for the neutral case. We also include a comparison result with respect to a cornerstone study, which can give a wonderful point of reference, but only for the sub-class of systems treated here.