In this paper, four observer-based distributed controllers are proposed for general linear multi-agent systems to achieve finite-time coordinated tracking under different situations. Specifically, for the cases of undirected communication graphs and directed communication graphs among the followers, both the situations of relative state measurement and relative output measurement among neighboring agents are considered. Under both kinds of communication topologies, when relative state information of the neighbors is available, distributed observer-based controllers are designed which achieve exact coordinated tracking in finite-time. When only relative output information is available, another finite time observer is introduced for each follower to estimate the relative state information. Together with the distributed controllers designed for the state feedback case, finite-time exact coordinated tracking can still be achieved in this situation. Numerical simulations are provided to illustrate the effectiveness of the proposed controllers. (C) 2016 Elsevier Ltd. All rights reserved.