Stability map of systems with three independent delays

In this work we examine an open problem: the stability robustness of LTI-systems with three time delays, which are rationally independent. A recent paradigm, called the cluster treatment of characteristic roots (CTCR) is used as the umbrella procedure, which claims to address the question here. It has never been shown earlier that the procedure is tractable for more than 2-delays. This is the first attempt to take up this challenging problem. In order to overcome the tractability problem, an efficient and novel algorithm is presented to form the first stage of the CTCR. Enabling concepts of "kernel and offspring hyperplanes" for the CTCR and two underlying propositions are also presented for this general class of problem. The main contribution of this document is that we demonstrate for the first time that the stability maps of a LTI-TDS (time delayed system) with three independent delays can be obtained efficiently, which is a very critical measure of the operation. An example case with 6th order LTI-TDS is presented to validate these claims