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This study addresses consensus problems of multi-agent systems (MASs) using dynamic output feedback control under both fixed and switching topologies. We aim to exploit the information structure for the consensusability of MASs. Necessary and sufficient conditions are presented in terms of detectability and stabilisability of the agents, graph topology, and some matrix inequality constraints. These conditions explicitly reveal how consensusability is affected by the intrinsic dynamics of the agents, the communication topology and available information. In addition, this paper provides several constructive procedures for protocol design to achieve consensus, and establishes the so-called separation principle, which simplifies the design procedure greatly.