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Summary: This paper is devoted to investigating the exponential synchronization of coupled Lur'e dynamical networks with multiple time‐varying delays and stochastic disturbance. The problem studied in this paper could be regarded as a kind of leader‐following synchronization issue. As the networks may suffer from certain impulsive disturbance, an effective distributed impulsive control protocol is proposed to synchronize the stochastic Lur'e dynamical networks. According to the comparison principle, the average impulsive interval, and the extended formula for the variation of parameters, sufficient conditions are derived for successful achievement of the network synchronization with consideration to different functions of impulsive effects. Furthermore, the exponential convergence rate is obtained based on the impulsive solution equation. In addition, finally, some numerical simulations are given to illustrate the validity of the control scheme and the theoretical analysis. [ABSTRACT FROM AUTHOR]