On Stability Crossing Set for General Systems with Three Delays—Part 1. Crossing Frequency Set

This is part 1 of a two-part article. The article describes the stability crossing set for linear time-delay systems of arbitrary order with three delays. The crossing frequency set, consisting of all frequencies where a pair of zeros of the characteristic quasipolynomial may cross the imaginary axis, is partitioned to Grashof set and Non-Grashof set of various types. It is found that the general characteristics of the stability crossing set is completely determined by the partition structure of the frequency crossing set. Part 1 describes the frequency crossing set. Part 2 describes the stability crossing set.