BIBO stability of fractional delay systems in the parametric space of delays

In this work, a novel method is proposed to study the BIBO stability of a fractional delay system. The characteristic equation of a fractional delay system with some transcendental terms has infinitely many roots. Applying D-subdivision method and the Rekasius substitution divide one-dimensional parametric space of the time delay to infinite intervals with finite unstable roots. The number of unstable roots in each interval is calculated with the definition of root tendency on the boundary of each interval. Two illustrative examples are presented to confirm the proposed method results.