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This paper deals with the H∞ control of spatially interconnected systems where homogeneous subsystems communicate with their neighbors over packet dropping channels. Both the robust stability analysis and controller synthesis problems are thoroughly investigated. At first, temporal forward and spatial shift operators are used to model the interconnected systems with random communication packet losses as discrete time-space linear multidimensional systems with Markovian jumping parameters. Analysis conditions are obtained which make the whole interconnected systems mean-square stable and achieve the prescribed H∞ disturbance attenuation performance. Then method for designing distributed state feedback controllers are presented, which could robustly mean-square stabilize the interconnected systems. The results take the form of computationally tractable linear matrix inequalities. Finally, a simulation example of multiple vehicle platoon control with the effect of communication packet losses is exploited to demonstrate the effectiveness of the proposed model and method.