First order approximation of the stability regions of time delay systems

A novel approach characterizing the way stability boundaries of time delayed dynamics enlarge or shrink is presented via a non-trivial development over an earlier study on first-order approximation of stability boundaries of delay-free systems. The uniqueness of the method is that it not only tackles regular points on such boundaries, but it also equally applies to singular points, which can be otherwise restrictive to treat by any other method known to the authors. The applicability of the approach without being limited to the dimension of the dynamics, the number of independent time delays and uncertain parameters is seen advantageous. Some example cases are provided to demonstrate the developed results.