This paper addresses the synchronization of follower agents’ state vectors with that of a leader in high-order nonlinear multi-agent systems. The proposed low-complexity control scheme employs high-gain observers to estimate higher-order synchronization errors, enabling the controller to rely solely on relative output measurements. This approach significantly reduces the dependence on full-state information, which is often infeasible or costly in practical engineering applications. An output feedback control strategy is developed to overcome these limitations while ensuring robust and effective synchronization. Simulation results are provided to demonstrate the effectiveness of the proposed approach and validate the theoretical findings.