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In this paper, the problem on outer synchronization is investigated for a class of mixed delayed complex networks by using the pinning control strategy. Together with some Lyapunov–Krasovskii functional and effective mathematical techniques, several conditions are derived to guarantee a class of complex networks with mixed delays to be outer synchronization. By proposing a novel functional condition which has not been proposed so far, further improved synchronization criteria are proposed. Finally, two examples are given to illustrate the effectiveness of the results.

Outer synchronization of a class of mixed delayed complex networks based on pinning control