In this paper, the output agreement problem for networks of dynamic agents based on high-order state-space descriptions is formulated and investigated. The agent dynamics is described by a time-invariant linear system with matrices A,B and C. The agreement problem, concerning the calculation of an agreed value based on the agent outputs, is proposed for such a class of networks. A linear state feedback control protocol for such networks is established for solving such an agreement problem. The control protocol includes two parts: a local state feedback controller and the interactions among the finite neighbors. A sufficient condition for the existence of such a control protocol is given. The corresponding design algorithm is presented, as well. Some numerical simulations are presented, which are consistent with our theoretical results.