Linear compensator designs based exclusively on input-output information are never robust with respect to unmodeled dynamics

The effects of unmodeled, higher-order dynamics or parasitics on the stability of linear control systems are investigated. A description is first given of a class of perturbations of a given state equation that cannot be distinguished from the original on the basis of input-output measurements alone. Then it is shown that given any plant-compensator pair, perturbations of each system of this type can always be found that destabilize the closed-loop configuration. The effect of destabilizing perturbations on output behavior is explored