Bounds of imaginary spectra for the stability assessment of a class of fractional-order systems with multiple delays

We treat the stability problem of a general class of fractional-order systems with multiple delays from a new perspective. To start with, we build a one-to-one correspondence between the imaginary spectra of original fractional-order systems and the special imaginary spectra of transformed systems with the auxiliary variable. Next, we show a novel improved frequency sweeping algorithm by using the Dixon resultant concept (IFS-DR) to calculate the so-called kernel hypersurfaces (KH). With these, the complete stability map is constructed by the Cluster Treatment of Characteristic Roots (CTCR) paradigm. We show that our presented approaches are valid and effective by the case study. In addition, the obtained stability map is compared to that of an integer-order time-delayed system. Finally, the results are verified by the Simulink-based simulations.