Stability crossing set for systems with three scalar delay channels

The characteristic function of a system with three scalar delay channels contains cross terms of different delays. This article studies the parameterization and geometric structure of the stability crossing set (the set of delay combinations with at least one characteristic root on the imaginary axis) for such systems. Understanding the structure of this set is crucial to the identification of stable regions in the delay parameter space using the D-subdivision method. The presence of the cross terms significantly complicates the analysis, and requires a quite different method than the case without these cross terms, and it involves more numerical computation.