A Practical Method for Stability Analysis of Linear Fractional-order Systems with Distributed Delay

In this paper, an effective method using the cluster treatment of characteristic roots (CTCR) technique is investigated for the stability analysis of a general class of fractional order systems (FOSs) with distributed delay. To conclude this goal, the characteristic equation of a FOSs with distributed delay is transformed to the characteristic equation of a FOSs with multiple delays; it is shown that the stability analyses of these two systems are equivalent. The magnitude of both delays, are considered to have non-zero values so that a comprehensive analysis is performed in the parametric space of delays. For obtaining stability switch curves also the procedure advanced clustering with frequency sweeping (ACFS) method is used. The proposed method of this article determines the stability map of such systems in the parametric space of delays accurately. The significance of this proposed method is in that, a comprehensive and precise stability analysis of such systems is not presented in the literature yet and this article is the first attempt to solve this challenging problem. The practicality and effectiveness of this method is shown here with an illustrative example.