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In this paper, a new scheme based on integral observer approach is designed for a class of chaotic systems to achieve synchronization. Unlike the proportional observer approach, the proposed scheme is demonstrated to be effective under a noisy environment in the transmission channel. Based on the Lyapunov stability theory, a sufficient condition for synchronization is derived in the form of a Lyapunov inequality. This Lyapunov inequality is further transformed into a linear matrix inequality (LMI) form by using the Schur theorem and some matrix operation techniques, which can be easily solved by the LMI toolboxes for the design of suitable control gains. It is demonstrated with the Murali-Lakshmanan-Chua system that a better noise suppression and a faster convergence speed can be achieved for chaos synchronization by using this integral observer scheme, as compared with the traditional proportional observer approach.