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A discrete perturbation observer (DPO) is suggested in state-space form for motion control applications. In existing disturbance observer design methods, the low-pass filter (so-called Q-filter) is central. However, the effect of the Q-filter on performance and robustness has not been clarified, specifically in the discrete-time domain. Considering the discrete Q-filter, with general order and inertia perturbations as a structured model uncertainty, we clarify how the performance and robustness of the perturbation observer are changed according to the variation of the Q-filter parameters and model parameter (i.e., inertia) perturbations in discrete control systems. Experimental results show the validity of the analysis and the effectiveness of the DPO.