A numerical method to find stability windows and unstable poles for linear neutral time-delay systems

This paper focuses on a numerical procedure to stability analysis of neutral time-delay systems with multiple commensurate delays. First, we give the asymptotic location of chains of poles, and conditions for their stability, for an arbitrary small delay. In this case, we can continue by using the root continuity argument, and by means of a simple substitution, find the location where roots cross the imaginary axis through numerical integration. Similarly, we can adapt the same technique to provide the location of all unstable poles (and eventually some stable ones). Several examples are presented and discussed.