We address in this paper the approximation problem of distributed delays.
Such elements are convolution operators with kernel having bounded support, and
appear in the control of time-delay systems. From the rich literature on this
topic, we propose a general methodology to achieve such an approximation. For
this, we enclose the approximation problem in the graph topology, and work with
the norm defined over the convolution Banach algebra. The class of rational
approximates is described, and a constructive approximation is proposed.
Analysis in time and frequency domains is provided. This methodology is
illustrated on the stabilization control problem, for which simulations results
show the effectiveness of the proposed methodology.