This paper focuses on a robust cooperative output tracking problem of networked power integrator systems. The dynamics of each system is considered as a nonlinear high-order power integrator whose linearised model is uncontrollable around its origin. It is proven via Lyapunov Theory that under some mild assumptions and graph structural properties, all agents' outputs in the network can be synchronised to a desired trajectory with a bounded error in the presence of external disturbances as well as model uncertainties. Moreover, the tracking performance can be tuned by appropriately choosing parameters within the controller. The proposed controller for each agent is in the essence constructed via backstepping technique consisting of three components: the state feedback of its own, the outputs of its neighbours and the information of the desired trajectory if connected, and thus in a distributed manner.