SummaryIn this paper, we address the mixed H2/H∞ synchronization control for the coupled partial differential systems. First, we introduce the synchronization error dynamics and transform the problem of mixed H2/H∞ synchronization control of coupled partial differential systems into the problem of mixed H2/H∞ stabilization of the synchronization error dynamics. Then, both the finite and infinite horizon cases for the mixed H2/H∞ synchronization control are considered. Sufficient conditions guaranteeing the existence of the solutions to the mixed H2/H∞ synchronization control problem are given via a standard completing square technique. When the states of the synchronization error systems are unavailable, the Lunberger observer is designed, and the observer‐based mixed H2/H∞ synchronization problem is investigated. Based on the solutions to the coupled differential Riccati equations, the optimal control for the observer‐based mixed H2/H∞ synchronization control is presented. One more time, both the finite and infinite horizon cases are studied under the observer situation. Copyright © 2016 John Wiley & Sons, Ltd.