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In this paper, we investigate the differential channel state information (CSI) feedback problem for a general multiple input multiple output (MIMO) system over time-correlated Rayleigh block-fading channels. Specifically, we derive the closed-form minimum differential feedback rate in the presence of channel estimation errors and quantization distortion. With the feedback-channel capacity constraint, we further study the ergodic capacity in a periodic feedback system in terms of the minimum differential feedback rate and the feedback interval. Through theoretical analysis, we find that there exists an optimal differential feedback interval to achieve the maximum ergodic capacity. Analytical results are verified by simulations in a practical periodic differential feedback system employing water-filling precoder and Lloyd's quantization algorithm.