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This paper is concerned with quantized state feedback H∞ control problem for networked control systems with random large delays which are less than or equal to two steps (two sampling periods). Here, the quantizations of the state feedback and the control input are considered, and the random large delays existing both from the sensor to the controller and from the controller to the actuator which are modeled as a function of stochastic variables are considered simultaneously. By using a novel model, the effect of the quantizations and the random large delays on the system performance is studied. The quantizer considered here is dynamic and composed of an adjustable zoom parameter and a static quantizer. A quantized H∞ control strategy is derived, with a condition on the quantization range and the error bound satisfied, such that the closed-loop system with quantization and random consecutive packet dropouts exponentially mean-square stable and with a prescribed H∞ performance bound. An example is presented to illustrate the effectiveness of the proposed method.