This paper discusses the stabilization of a class of linear infinite-dimensional systems, described by distributional convolution equations with bounded support. In particular this includes time-delay systems containing several time-varying delays in the state and the input. The system is stabilized using a linear time-invariant memoryless feedback law, and closed-loop stability is proved by means of a classical quadratic Liapunov functional. Sufficient conditions for stabilizability and design algorithms for a stabilizing feedback amplifier matrix are derived.