Approximation of distributed delays

Abstract

International audienceIn 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

Stability of linear continuous‐time difference equations with distributed delay: Constructive exponential estimates

“…In this section, we illustrate our results with the control of the interconnection of two systems governed by the 1D wave equation; see, for instance, [18]. The coupling is achieved by control laws involving distributed delays, which are well known to successfully address stabilization problems; see, for instance, [19] and the references therein. This interconnection is shown in Figure 1: The square gray nodes characterize pointwise and distributed delays with kernel in P C .OE0; r N /; R n /, while the other nodes of the network are dynamical systems of second-order linear hyperbolic partial differential equations @´´ k .´; t / 1 c 2 @ t t k .´; t / D 0; t > 0;´2 .0;`k/ (56)…”