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We consider the stabilization problem for a kind of networked control systems in discrete-time domain with random delays. The sensor-to-controller and controller-to-sensor delays are modeled as two Markov chains, and the resulting closed-loop systems are jump linear systems with two modes. The necessary and sufficient conditions on the existence of the stabilizing controllers are established. It is shown that the state-feedback gains are different with different modes. An iterative linear matrix inequality (LMI) approach is employed to calculate the state-feedback gains.