Stability Analysis of LTI Fractional-order Systems with Distributed Delay

This paper proposes a method for the stability analysis of a class of fractional-order systems (FOSs) with distributed delay using the cluster treatment of characteristic roots (CTCR) technique. The proposed method is important since no method analyzes the stability of linear FOSs with a distributed delay. For this purpose, we shall show that the stability of a FOS with a distributed delay is equivalent to a class of FOSs with multiple single delays. Thus, the system stability can be comprehensively declared in the parametric space of the distributed delays. Next, the procedure advanced clustering with the frequency sweeping method is employed as the first step to the CTCR to determine stable switching boundaries. Eventually, the practicality and effectiveness of the proposed approach are shown in an illustrative example.