Stable regions in the parameter space of delays for LTI fractional-order systems with two delays

This paper studies fractional-order systems of retarded type with two independent delays, and determines the stability regions in spaces of delays. In this approach, an auxiliary polynomial is employed to calculate all purely imaginary roots of the characteristic equation of the system on the imaginary axis. Since roots of the characteristic equation are continuous with respect to delays, these purely imaginary roots determine the stability regions in delay space. Also, the necessary and sufficient condition for stability independent of delays is developed for the systems. Furthermore, a simple inequality constraint is established to obtain pure imaginary poles of the scalar systems. Finally, the obtained results are illustrated by two examples, and the method is applied to analyze the model of human immunodeficiency virus type 1 infection.