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Controllability is the key issue of multi-agent systems research, mainly includes the structural controllability and exact controllability.In this paper, the algebraic conditions of exact controllability analysis are summarized.Under the relative and absolute protocol, the algebraic conditons of a multi-agent systems controllability are analyzed by using graph theory and matrix methods.A necessary and sufficient conditions for a multi-agent dynamics system to be controllable are presented.And some new linear algebra conditions is also presented.