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Abstract In this paper, a memristor-based hyperchaotic system is introduced. Considering time delays between the drive system and the response system in the process of synchronization, this paper designs one kind of flexible sandwich controller, which includes a rest in the sandwich structure, to realize the synchronization between two memristor-based hyperchaotic systems. Based on Lyapunov stability theory, matrix inequality, sandwich control and considering time delays, the exponential synchronization conditions for the memristor-based hyperchaotic systems with time delays via sandwich control are given. Finally, simulation results are displayed to verify the effectiveness and feasibility of this method.