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This paper focuses on the stability analysis of generalized neural networks with time-varying delays. First, a novel augmented Lyapunov-Krasovskii functional (LKF) is constructed by introducing a couple of integral vectors. Second, by utilizing the novel augmented LKF and a generalized free-weighting-matrix integral inequality, two further stability criteria are presented in this paper. Third, a less conservative stability condition by refining the allowable delay set is introduced. Finally, the four well-known numerical examples are given to demonstrate the effectiveness and improvements of the proposed methods.