Stabilizing first-order controllers with desired stability region

Abstract

In this paper, we determine the set of all stabilizing first-order controllers that place the poles of the closed-loop system in a desired stability region. The solution is based on a generalization of the Hermite-Biehler theorem applicable to polynomials with complex coefficients and the application of a modified stabilizing gain algorithm to three subsidiary plants. The method given is also applicable to PID controllers.