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This paper presents an H∞ controller design method for networked control systems (NCSs) with bounded packet dropouts. A new model is proposed to represent packet dropouts satisfying a Markov process and late-arrival packets. The closed-loop NCS with a state-feedback controller is transformed into a Markov system, which is convenient for the controller synthesis. Two types of state-feedback control laws are taken into account. Sufficient conditions on the existence of controllers for stochastic stability with an H∞ disturbance attenuation level are derived through a Lyapunov function dependent on the upper bound of the number of consecutive packet dropouts. A numerical example is finally provided to show the effectiveness of the proposed method.