Stability map of fractional delay systems in the parametric space of delays and coefficient

In this paper, we examine an open problem: The stability analysis of fractional order systems with uncertain parameters in both time-delay space and coefficient space. It is evident from the literature that the stability assessment of this class of dynamics remains unsolved. The Rekasius transformation is used as a connection between time-delay space and coefficient space. For generating potential stability switching curves (PSSC) an efficient procedure is proposed to extend the paradigm called, advanced clustering with frequency sweeping (ACFS), to the determination of stability regions in coefficient-delay space. We show that this methodology analytically reveals all possible stability regions exclusively in the space of the delay and coefficient. Two examples are presented to highlight the proposed approach.