This paper studies the global leader-following consensus problem for a multi-agent system with bounded controls. The follower agents and the leader agent are all described by a general linear system. Both a bounded state feedback control law and a bounded output feedback control law are constructed for each follower agent in the group. The feedback law for each input of an agent uses a multi-hop relay protocol, in which the agent obtains the information of other agents through multi-hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of eigenvalues at the origin and the number of pairs of non-zero imaginary eigenvalues of the sub-system corresponding to the input, and the feedback gains are constructed from the adjacency matrix of the communication network. It is shown that global leader following consensus is achieved under these feedback control laws when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower. (C) 2016 Elsevier Ltd. All rights reserved.