Complete Stability Map of First Order - Two Time Delay Systems with Delay Cross-Talk

First order linear time invariant dynamics is taken into account with two delays. What makes this class of dynamics unique, from the stability perspective, is the added term representing the cross-talk between the two delays. Such delay cross-talk may practically arise due to interference of controller gains in full state feedback with states being inevitably delayed. This class of systems can be treated for their stability by a unique procedure, which is recently developed, known as cluster treatment of characteristic roots (CTCR). In the text we present several case studies to display the steps and the strengths of CTCR. We also include some comparison results with respect to a cornerstone study of Hale and Huang, 1993, which gives a wonderful point of reference for this class of systems, however without the delay cross-talk effect.