Abstract
Stability of systems with a single delay and delay-dependent coefficients is studied along the line of the τ-decomposition approach. Criteria for determining crossing directions of imaginary characteristic roots with possibly multiplicity are presented, with which system stability for any given delay value can be determined in a systematic way. In contrast to the previous research on this type of systems, our analysis is based on a novel two-parameter framework. With the new geometric insight, stronger criteria concerning the crossing direction of imaginary characteristic roots with possibly multiplicity can be obtained using simplified and intuitive arguments. The stability analysis procedure is illustrated with an example inspired by biological applications.
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