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In this paper, the output consensus of a class of linear heterogeneous multi-agent systems with unmatched disturbances is considered. Firstly, based on the relative output information among neighboring agents, we propose an asymptotic sliding-mode based consensus control scheme, under which, the output consensus error can converge to zero by removing the disturbances from output channels. Secondly, in order to reach the consensus goal, we design a novel high-order unknown input observer for each agent. It can estimate not only each agent’s states and disturbances, but also the disturbances’ high-order derivatives, which are required in the control scheme aforementioned above. The observer-based consensus control laws and the convergence analysis of the consensus error dynamics are given. Finally, a simulation example is provided to verify the validity of our methods. [ABSTRACT FROM AUTHOR]