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This paper studies the decentralized H∞ control problem for a class of compartmental networks, where the controller gain matrix is required to be diagonal and elementwise restricted. To solve the problem, we first propose a novel characterization under which the closed-loop system is asymptotically stable with a prescribed H∞ performance. Then, a necessary and sufficient condition for the existence of a required controller is obtained, and an iterative linear matrix inequality approach is developed to solve the design condition. Moreover, a D-K iteration method is presented to optimize the initial value such that the solvability of the original problem can be further enhanced. Finally, the obtained results are illustrated through an application to a simple air traffic flow network model.