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This paper studies the problem of sampled-data control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems with time delays. It is assumed that the sampling periods are arbitrarily varying but bounded. In order to take full advantage of the available information about the actual sampling pattern, a novel Lyapunov functional is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Based on the Lyapunov functional, an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems. The desired sampled-data controller is designed by a linear matrix inequality approach. The effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of Chua's circuit and neural network.