The class of dissipative hyperbolic distributed parameter systems is defined here; it includes many physical phenomena such as mechanically flexible structures and certain linear wave propagation problems. Feedback control theory for this class of systems is investigated. Although some results on infinite dimensional controllers are presented, the emphasis is on practical (i.e., finite dimensional) controllers based on reduced-order models of the distributed parameter system and the closed-loop operation of such controllers in the actual system. Sufficient conditions, in terms of “spillover” bounds for the unmodeled residuals, are presented for exponentially stable closed-loop operation.