Approximation of distributed delays

In this paper, we address the approximation problem of distributed delays. These 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 working on the convolution Banach algebra, a constructive approximation is proposed. Analysis in time and frequency domains is provided. This methodology is illustrated on the stabilization control for time-delay systems.