Delay range stability of a class of distributed time delay systems

This paper is dedicated to the stability analysis of a class of uncertain distributed delay systems, the kernel of which can be modeled as a polynomial function of the delay. The results are constructed by rewriting the system as an uncertain interconnected model. Appropriate robust control tools, i.e. quadratic separation, are then used to address the stability issue. To this end, some relations that highlight relevant characteristics of the delayed term are added to the interconnected model leading then to the conservatism reduction. Finally, numerical examples show the effectiveness of the proposed method.