A Bode Plot Characterization of All Stabilizing Controllers

In this technical note, we consider continuous-time control systems and present a new characterization of the Nyquist criterion in terms of Bode plots of the plant and the controller. This gives a non-parametric, and model independent characterization 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.