PID controller design for robust performance

This paper is devoted to the problem of synthesizing proportional-integral-derivative (PID) controllers for a given single-input single-output plant so that the closed-loop system is robustly stabilized and the desired performance specifications are satisfied despite plant 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. In particular, it is shown that for a fixed proportional gain, the set of admissible integral and derivative gains is a union of convex sets.