This technical note addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. The existing methods typically rely on global information, such as the smallest real part of the nonzero eigenvalues of the Laplacian matrix, which is not suitable for fully distributed implementation. The authors propose a distributed adaptive consensus protocol that uses only the agent dynamics and the relative states of neighboring agents to achieve leader-follower consensus in the presence of a leader with a zero input. The protocol is independent of any global information of the communication graph, making it fully distributed. The paper also extends the protocol to the case with multiple leaders, solving the containment control problem where the states of the followers are driven into the convex hull spanned by the states of the leaders. The effectiveness of the proposed protocol is demonstrated through a simulation example.This technical note addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. The existing methods typically rely on global information, such as the smallest real part of the nonzero eigenvalues of the Laplacian matrix, which is not suitable for fully distributed implementation. The authors propose a distributed adaptive consensus protocol that uses only the agent dynamics and the relative states of neighboring agents to achieve leader-follower consensus in the presence of a leader with a zero input. The protocol is independent of any global information of the communication graph, making it fully distributed. The paper also extends the protocol to the case with multiple leaders, solving the containment control problem where the states of the followers are driven into the convex hull spanned by the states of the leaders. The effectiveness of the proposed protocol is demonstrated through a simulation example.