Robust stability analysis for fractional-order systems with time delay based on finite spectrum assignment

In this paper, the robust stability of a fractional-order time-delay system is analyzed in the frequency domain based on finite spectrum assignment (FSA). The FSA algorithm is essentially an extension of the traditional pole assignment method, which can change the undesirable system characteristic equation into a desirable one. Therefore, the presented analysis scheme can also be used as an alternative time-delay compensation method. However, it is superior to other time-delay compensation schemes because it can be applied to open-loop poorly damped or unstable systems. The FSA algorithm is extended to a fractional-order version for time-delay systems at first. Then, the robustness of the proposed algorithm for a fractional-order delay system is analyzed, and the stability conditions are given. Finally, a simulation example is presented to show the superior robustness and delay compensation performance of the proposed algorithm. Moreover, the robust stability conditions and the time-delay compensation scheme presented can be applied on both integer-order and fractional-order systems.