Hybrid control has in the recent years drawn considerable attention in academia as it poses a large number of theoretical and computational challenges. The interested scientific community has proposed various methods to address some of the problems related to modeling and control of hybrid systems. The conceptual validation of these methods has been by far illustrated through the use of typically simple academic examples. In this paper the hybrid systems is treated as a single directed topological space, and presents a refrigeration system as a benchmark that should be useful as a platform for the development of new ideas and a comparison of methods. Based on the model of this coupled hybrid system, we analyze the synchronization of the controllers in terms of the theories about topological space and Section Mapping.