On the Stability of Fractional Order Systems of Neutral Type

Abstract

The aim of this study is to offer a new analytical method for the stability testing of neutral type linear timeinvariant (LTI) timedelayed fractionalorder systems with commensurate orders and multiple commensurate delays. It is evident from the literature that the stability assessment of this class of dynamics remains unsolved yet and this is the first attempt to take up this challenging problem. The method starts with the determination of all possible purely imaginary characteristic roots for any positive time delay. To achieve this, the Rekasius transformation is used for the transcendental terms in the characteristic equation. An explicit analytical expression in terms of the system parameters which reveals the stability regions (pockets) in the domain of time delay has been presented. The number of unstable roots in each delay interval is calculated with the definition of root tendency (RT) on the boundary of each interval. Two example case studies are also provided, which are not possible to analyze using any other methodology known to the authors.