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Recently, dynamic adaptive streaming over HTTP (DASH) has been widely deployed on the Internet. However, the research about DASH over multiple content distribution servers (MCDS-DASH) is limited. Compared with traditional single-server DASH, MCDS-DASH is able to offer expanded bandwidth, link diversity, and reliability. It is, however, a challenging problem to smooth video bitrate switching over multiple servers due to their diverse bandwidths. In this paper, we propose a block-based rate adaptation method considering both the diverse bandwidths and feedback buffered video time. In our method, multiple fragments are grouped into a block and the fragments are downloaded in parallel from multiple servers. We propose to adapt video bitrate at the block level rather than at the fragment level. By dynamically adjusting the block length and scheduling fragment requests to multiple servers, the requested video bitrates from the multiple servers are synchronized, making the fragments download in an orderly way. Then, we propose a control-theoretic approach to select an appropriate bitrate for each block. By modeling and linearizing the rate adaption system, we propose a novel proportional-derivative controller to adapt video bitrate with high responsiveness and stability. Theoretical analysis and extensive experiments on our network testbed and the Internet demonstrate the good efficiency of the proposed method.