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This paper presents a controller design algorithm for a class of networked control systems with random delay based-on variable-period sampling model, where the sensor to controller delay is modeled as a Markov chain. Since the time delay varies randomly, the time delay to occur at current sampling step is regarded as the sampling period between current sampling step and next sampling step. Using the properties of Markovian chain, the next step time-delay is calculated according to the current time-delay and probability transition matrix. The resulting closed-loop systems are jump linear systems. The necessary and sufficient conditions on the existence of the stabilizing controllers are established. It has been shown that the controller gains can be obtained by solving the LMIs using an iterative linear matrix inequality (LMI) approach. A simulated example is included to show the effectiveness of the proposed algorithm and interesting results have been obtained.