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The paper addresses stability analysis of discrete-time delayed systems. The delay is assumed time-varying and its value bounded in a known interval. By using the same Lyapunov-Krasovskii functional as used in a recent paper, a set of sufficient LMI conditions is obtained from using solely the Jensen inequality treatment to ensure asymptotical stability of the considered system. The conditions are shown to be equivalent to the ones obtained recently by using the Jensen inequality and the free-weighting matrix techniques. The delay partition technique is exploited further to reduce the conservativeness induced by the Jensen inequality treatment. Simulation results show the benefit of the used delay partition approach.