Abstract
In this paper we give an algorithm that determines the set of all stabilizing proportional-integral-derivative (PID) controllers that places the poles of the closed loop system in a desired stability region S. The algorithm is applicable to linear, time invariant, single-input singleoutput plants. The solution is based on a generalization of the Hermite-Biehler theorem applicable to polynomials with complex coefficients and the the application of a stabilizing gain algorithm to three auxiliary plants.