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Based on the Lyapunov stability theory, this paper mainly investigates the H∞ synchronization problem for semi-Markovian jump neural networks (semi-MJNNs) with randomly occurring time-varying delays (TVDs). The continuous-time semi-MJNNs, where the transition rates are dependent on sojourn time, are introduced to make the issue under our consideration more general. One of the main characteristics of our work is the handling of TVDs. In addition to using the improved Jensen inequality and thedoi:10.1155/2018/8094292 fatcat:qqif7e34qzh3ve2wejvaswi22q