The paper investigates the input—output energy balances in linear dynamical systems subjected to unmodelled dynamics for which an aprioriknowledge is needed in terms of frequency and time-domain specifications. A discussion about the synthesis of linear controllers in the linear and time-invariant case is also given. The controllers have robustness properties, in the sense that the system subjected to unmodelled dynamics has a close behaviour, in an input-output energy sense, to the nominal (perfectly modelled) case.