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In this study, the observer‐based output feedback H∞ control problem is investigated for the two‐dimensional (2D) networked control system (NCS) in form of Fornasini–Marchesini second model. The communication from the controller to the actuator is carried out through a shared network medium, where only one signal gets the network access at each transmission instant. To avoid data collisions, the periodic scheduling protocol is employed to assign the network access priority to the actuator in chronological order. To improve the reliability of data transmission, redundant channels are applied to deliver the measurement observed by the sensor to the controller. The aim of the addressed problem is to design an observer‐based output feedback controller so that the considered 2D NCS satisfy a predefined H∞ performance index. Sufficient condition is given to ensure the H∞ performance of the closed‐loop system via the Lyapunov theory and stochastic analysis. Moreover, the observer‐based output feedback controller is designed to achieve the desired H∞ performance index, under which the controller parameters are determined by solving certain optimisation problems. Finally, a numerical example is given to demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]