In this paper, the output synchronization problem is investigated for a heterogeneous network. Specifically, the non-identical followers are affected by parameter perturbations and controlled to achieve output synchronization with an uncertain leader. We use the adaptive control theory and the robust output regulation theory to solve this problem. The proposed method includes two stages, which is similar to the separation principle. In the first stage, the designed distributed control law and adaptive control law can force that the outputs of the reference generators locally exponentially converge to the output of the leader. In the second stage, the robust output regulation control law is applied in a decentralized control model, to guarantee that the output of each non-identical follower robustly tracks the output of the corresponding reference generator. The main contributions of this paper are the constructions of adaptive reference generators in the first stage and robust regulators in the second stage. Examples are presented to show the effectiveness of the proposed design techniques. (C) 2016 Elsevier Ltd. All rights reserved.