On the robustness of compensator designs based exclusively on input-output information

We are interested in the effects of unmodelled parasitics or high-frequency phenomena on the closed-loop performance of a given control system. We show that, if a compensator design is based entirely on input-output characteristics of the open-loop system, it is always possible that such unmodelled aspects of the plant may destabilize the closed-loop configuration. The proof is based on Hurwitz conditions.