An overview of stability crossing set for systems with scalar delay channels

The stability crossing set is defined as the set of parameters such that the system characteristic equation has at least one imaginary root. The description of the stability crossing set is crucial in the stability analysis of time-delay systems using the D-subdivision method, especially for systems with multiple delays. This article provides an overview of recent research results on determining the stability crossing sets of systems with multiple delays. In particular, complete parameterization and geometric characterization of the stability crossing set are possible for systems with two or three variable scalar delay channels.