A frequency response parametrization of all stabilizing controllers for discrete time systems

In this paper, we present new results that are useful for the synthesis of fixed order digital controllers from plant frequency response data. The main result is a nonparametric characterization of the frequency response of arbitrary order rational discrete time stabilizing controllers. This result shows that the frequency response of the inverse plant imposes constraints on the magnitude, phase, and rate of change of phase of the digital controller´s frequency response at certain frequencies.