The terminal energy router is an important piece of energy routing equipment in the energy internet. The most effective way to construct its topology is to use a solid-state transformer based on power electronic converter technology. After the energy routing topology is determined, the control technology directly determines its operational characteristics. This paper uses switching system theory based on hybrid system theory to control the energy routing of the terminal energy router. First, the topology and working principle of the router are analyzed in detail. Then, the switching system behavior characteristics of are analyzed, and a switching system model is established. Secondly, combined with space vector pulse width modulation technology, a multi-mode switching control method is proposed. Finally, a model is built through Matlab/Simulink simulation platform to verify the effectiveness of the proposed method. Theoretical analysis and simulation show that this method fully considers the interaction between discrete and continuous variables in the operation of the router, and has the characteristics of short switching time and stable switching process. This optimizes the dynamic regulation characteristics and improves control tracking speed and accuracy. This work is supported by the National Natural Science Foundation of China (No. 51708194 and No. 51507014).