Power mapping-based stability analysis and order adjustment control for fractional-order multiple delayed systems

This article investigates the asymptotic stability of a general class of fractional-order multiple delayed systems to evaluate the delay robustness. We establish a one-to-one spectral connection between the original fractional-order system and the transformed one under the power mapping. The applicability of the Cluster Treatment of Characteristic Roots paradigm to the transformed dynamics is proved by this connection. Then, we utilize the Dixon resultant-based frequency sweeping framework to create the complete stability map. The results demonstrate that the order adjustment control significantly enhances the control flexibility and brings unlimited possibilities for the improvement of the delay robustness. Finally, we inspect the stability preservation problem when using the integer-order approximations for practical implementation.