Stability intricacies of two-delay linear systems in the presence of delay cross-talk

An improved technique to stabilise a class of first-order linear time-invariant dynamics with two delays is presented. It proposes to design a controller in which delay cross-talk feature (or delay coupling) is utilised to enhance the system´s stability characteristics. The authors present some comparative observations vis-a´-vis an earlier pioneering study, which is a widely used point of reference for this class of systems, however, without the delay cross-talk effect. Furthermore, the treatment here profits from a recently introduced methodology, called the ´cluster treatment of characteristic roots (CTCR)´, for the stability assessment of these systems, differently from the earlier suggested procedures. With the introduction of the delay cross-talk term, the authors show that the new system may become stable for larger delay zones, which is otherwise impossible. In the text, we present several case studies to display the outcome of such a tool.