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This paper presents a network-based model predictive controller design strategy for spatially distributed systems (SDSs), where control input quantization over a digital network is considered. To simplify the control design, the spatiotemporal control problem is transformed to a temporal one. Basing on the temporal model, a robust model predictive controller is designed to provides an efficient solution to the quantized control issues for spatially distributed system, where the quantization problem for control design is solved by a robust control problem with sector bounds uncertainties. The efficiency of the proposed method was shown through a network control problem based on a typical SDS.