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For descriptor multi-agent systems with fixed topology and agents described by general descriptor linear time-invariant systems, necessary and sufficient conditions of consensusability with respect to a set of admissible consensus protocols are proposed using the tools of algebra, graph and descriptor linear system theory. The consensusability conditions depend on both the structure properties of each agent's dynamics and the topology within the descriptor multi-agent systems. Designing an output feedback control law can guarantee that the studied descriptor multi-agent system is consensusable with respect to a given admissible set. A provided example indicates the applicability of the proposed approach.