Dominant pole analysis of neutral-type time delay positive systems

This paper is concerned with dominant pole analysis of neutral-type time delay positive systems (TDPSs). The neutral-type TDPS of interest is constructed by feedback connection between a finite-dimensional linear time-invariant positive system (FDLTIPS) and the pure delay, where the FDLTIPS has a nonzero direct feedthrough term. It has been shown very recently that this neutral-type TDPS is asymptotically stable if and only if its delay-free finite-dimensional counterpart is stable and admissible, where the latter means that the direct feedthrough term is Schur stable. This result in particular implies that the stability is irrelevant of the length of the delay. However, it is strongly expected that convergence or divergence rate depends on the delay length and this is the motivation for the dominant pole analysis. In this paper, we show that one of the dominant poles of the neutral-type TDPS is real irrespective of the stability, and we derive closed-form formulas that relate the real dominant pole with the delay length for both stable and unstable neutral-type TDPSs.

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