Stabilizing first-order controllers for n-th order all pole plants with time delay

In this paper, the stabilizing regions of a first-order controller for an all pole system with time delay are determined via parametric methods. First, a necessary condition is used to determine the admissible ranges of one of the controllerpsilas parameters. Then, for a fixed value of this parameter the stabilizing regions in the remaining two parameters are determined using the D-decomposition method. The approach used can be applied to determine stabilizing regions of a PID controller. Finally, examples are given to illustrate the proposed approach.