In today's complex embedded systems not all applications are running all the time, but depend on the operational mode. By incorporating knowledge about the temporal behavior of such multi-mode systems, it is possible to share hardware by means of partial reconfiguration, and thus, reduce costs and improve performance. In this paper, we specify the temporal behavior of the functionality by applying known models based on state machines. In addition, we introduce an architectural model that allows to express the characteristics of nowadays partially reconfigurable architectures, focusing on FPGAs. We develop a symbolic encoding of this novel system specification, which allows to perform a unified system synthesis for allocation, binding, placement of partially reconfigurable modules, and routing the on-chip communication. The proposed encoding enables the use of sophisticated optimization techniques, coupling a SAT solver with a Multi-objective Evolutionary Algorithm. The proposed methodology is highly applicable for building multi-mode systems on advanced reconfigurable technology. We demonstrate this by experiments on test-cases from the image processing domain applying state-of-the-art technology. The results show the superiority of the presented approach in terms of run-time and quality of the found solutions compared to existing system synthesis approaches.