Delay systems represent a class of infinite-dimensional systems [1, 2, 3] largely used to describe various types of processes such as transport and propagation phenomena [5, 6] or population dynamics [4, 7, 8]. Roughly speaking, any interconnection of physical systems handling and transferring material, energy or information is intrinsically subject to delays. If, at the origin, such a phenomenon was related to developments specific to control engineering and if, in most cases, the delay effects were neglected or approximated, it becomes more and more involved in characterizing and/or improving various performances in dynamical systems. Thus, for example, in communication systems, data transmission is always accompanied by some nonzero time-interval between the initiation and the delivery of the corresponding message or signal, which can be 'transferred' with or without any processing. In such a case, huge transmission delays will reduce the qualitative behavior of the system, as, for example, its 'ability' to treat large amount of data, and thus the performances of the transmission systems.