I. Introduction
This paper is devoted to the stability analysis of linear time-delay systems, which represent a wide class of systems arising in many applications such as in biology, traffic control, engineering, cyber-physical systems, or networked control systems (see for instance the books and survey papers [2], [3], [7], [22]). Compared to the delay-free case, the difficulties when studying time-delay systems mainly come from the infinite dimensional nature of this class of systems, which require a dedicated analysis.