Stability of distributed delay systems via a robust approach

This paper is dedicated to the stability analysis of a class of distributed delay systems with a non constant kernel. By the use of appropriate orthogonal polynomials, this kernel is expressed as the sum of a polynomial and an additive bounded function. The resulting system is then modeled by an interconnected system between a nominal finite dimensional linear system and a infinite dimensional system. This last system is considered as a structured uncertainty and embedded into some well defined structured uncertainties. Appropriate robust control tools, i.e. quadratic separation, are then used to address the stability issue. Finally, numerical examples show the effectiveness of the proposed method.