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In this paper, the output feedback-based bipartite consensus problem for MASs of unstable heat equations is investigated. The interactions of participating individuals are cooperative and competitive on an undirected graph. In order to achieve accurate estimation of system state, a distributed state observer is proposed. By introducing a reversible transformation, the observer system is transformed into a new system, and the controller based on the new system states is designed, which guarantees the well-posedness and stability of the considered control system and the observer system due to the invertibility of the presented transformation. Similarly, the bipartite consensus is analysed and proved. Finally, the validity of the proposed method is verified by simulation examples. [ABSTRACT FROM AUTHOR]