Stability Analysis of Neutral Type Time-Delay Positive Systems with Commensurate Delays

Recently, the author derived a necessary and sufficient condition for the asymptotic stability of neutral type time-delay positive systems (TDPSs), where the neutral type TDPS of interest is given by a feedback connection between a finite-dimensional LTI positive system and the pure delay The goal of this paper is to extend this result to neutral type TDPSs with multiple commensurate delays. To this end, we first represent a neutral type TDPS with multiple commensurate delays as a neutral type TDPS with a single delay, by augmenting input and output signals in the feedback connection. By this conversion, we can readily apply the latest result already established for single delay neutral type TDPSs. As the main result, we show that a neutral type TDPS with commensurate delays is stable if and only if its delay-free counterpart is stable and an additional “admissibility” condition is satisfied. This result in particular implies that the stability is irrelevant of the length of delays.