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

In this paper, we present an alternative and new interpretation of the Nyquist criterion in terms of Bode plots of the plant and the controller. This result gives a nonparametric characterization of the frequency response of arbitrary order stabilizing controllers. The result shows that the frequency response of any stabilizing controller must satisfy constraints on its magnitude, phase, and rate of change of phase at certain frequencies that are imposed by the frequency response of the inverse plant.