Summary: Vibrational systems, characterized by their second-order or ``spring-mass'' nature, occur throughout engineering. Examples range from lightly damped structures, such as the proposed space station, to regional power system models. While the study of such vibrational systems has a long and rich history, concern has traditionally focused on the properties of passive, uncontrolled systems. The growing need to actively control large, complex systems of this type leads us to the study of controlled vibrational systems. We provide stability assuring constraints for compensator design. These constraints directly use the initial system model, thus avoiding the need for order reduction techniques with the associated problems of ``spill-over'' from the full to the reduced system model.