Stability analysis of time-delayed linear fractional-order systems

In this article, an exact and robust method for the determination of all the possible stability regions in the parametric space has been presented for the fractional order systems with time delay. Using the approach presented in this study, first, the transcendental terms have been eliminated from the characteristic equation and then, all the locations on the imaginary axis crossed by the roots and also their direction of crossing have been calculated. Finally, the concept of the stability as a function of the time delay has been described for a general class of linear fractional order systems with several commensurate delays. Prior to the conclusion, several examples have been given to validate the results of the proposed approach.