<p>This paper is devoted to the asymptotic consensus tracking problem for a class of multi-agent systems (MASs) subject to dynamic quantization, unmeasured states, and unknown disturbances. To address the main design challenge that the desired tracking trajectory is accessible only to a subset of agents while the system faces uncertainties simultaneously, a hierarchical control structure is proposed to decouple distributed desired trajectory tracking from local robust control. In the estimation layer, a filter is introduced for each agent. By incorporating local estimators about the bounds of the desired trajectory, a local controller is designed for the filter to ensure that its output asymptotically tracks the desired trajectory. In the backstepping control layer, a finite-level uniform quantizer with a time-varying scaling function is adopted to reduce data transmission. Based on the quantized signal, a state observer and a disturbance observer are designed to estimate states and disturbances, respectively. When prior knowledge of the initial conditions for the MAS is unknown, to ensure transient performance of the tracking error between each agent’s output and the filter’s output, a prescribed-time scaling function is constructed. Then, together with an improved Lyapunov function, the proposed backstepping control scheme guarantees that this tracking error converges to a prescribed accuracy within a preset time and asymptotically converges to zero. With both layers, asymptotic consensus tracking is thereby achieved. Finally, the effectiveness of the proposed approach is validated by simulation results.</p>