This paper deals with the synthesis of symbolic controllers for interconnected sampled-data systems where each component has its own sampling period. A compositional approach based on continuous-time assume-guarantee contracts is used. We provide sufficient conditions guaranteeing for a sampled-data system, satisfaction of an assume-guarantee contract and completeness of trajectories. Then, compositional results can be used to reason about interconnection of mul-tiperiodic sampled-data systems. We then show how discrete abstractions and symbolic control techniques can be applied to enforce the satisfaction of contracts and ensure completeness of trajectories. Finally, theoretical results are applied to a vehicle platooning problem on a circular road, which show the effectiveness of our approach.