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This paper deals with the problem of state estimation for discrete-time recurrent neural networks with interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. A delay-range-dependent condition for the existence of state estimators is proposed. Via available output measurements and solutions to certain linear matrix inequalities, general full-order state estimators are designed that ensure globally asymptotic stability. Two illustrative examples are given to demonstrate the effectiveness and applicability.