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We consider compartmental systems described by conservation equations. We give sufficient conditions, in the form of linear matrix inequalities, for the existence of decentralized controllers guaranteeing a prescribed level of closed-loop performance, in the context of model-matching. This decentralized design method is new in that it allows to directly handle the natural constraints on the state and input of such systems, with no added conservatism. The control design method is illustrated by an application to an Eulerian model of air traffic flow.