On Monotonic and Nonmonotonic Step Responses in Fractional Order Systems

This paper investigates the step responses of fractional order systems in the viewpoint of extrema existence in such responses. It is proven that a fractional order system with a commensurate order between zero and one has an extrema-free step response if its integer counterpart has such a step response. In addition, it is shown that the step response of a stable fractional order system with a commensurate order between one and two cannot be monotonic. Based on these achievements, some further results on the step response of different classes of fractional order systems are presented.