PID controller design for robust performance

This note is devoted to the problem of synthesizing proportional-integral-derivative (PID) controllers for robust performance for a given single-input-single-output plant in the presence of uncertainty. First, the problem of robust performance design is converted into simultaneous stabilization of a complex polynomial family. An extension of the results on PID stabilization is then used to devise a linear programming design procedure for determining all admissible PID gain settings. The most important feature of the proposed approach is that it computationally characterizes the entire set of the admissible PID gain values for an arbitrary plant.