This paper investigates the problem of bipartite formation control for high-order linear multi-agent systems in the context of switching communication topologies and unobservable states. Firstly, a full-state observer is constructed to observe the states of the completely unobservable system. Then, based on the state observer, a distributed controller for the multi-agent system is designed, incorporating linear product theory with distributed control to reconstruct the system. The paper applies graph theory, matrix analysis, and Lyapunov theory to analyze the stability of the reconstructed system and provides the conditions for the average dwell time of the connected graph to achieve the final bipartite formation under switching communication topologies. Additionally, in the adversarial network environment, the conditions for feasible time-varying formation are given when the system state is unknown. Furthermore, a bipartite formation compensation function is introduced into the controller to increase the number of bipartite formations that the system can form, which is of practical significance. Finally, the effectiveness of the proposed method is verified through numerical simulations.