Stability analysis for fractional-order PD controlled delayed systems

This paper aims to solve all possible fractional PD controllers to stabilize the given system. Robust stability with margins, namely phase margin and gain margin, is also considered. The obtained parameters׳ regions are described on delay-parameter plane. Figures are obtained by critical boundary, which reflects that controlled system׳s critical characteristic root. Critical boundary is analyzed via D-decomposition method. In this paper, delay is processed as a revealed element by Rekasius transformation. An example is given to illustrate the proposed method.