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This brief deals with the problem of observers design for Lipschitz nonlinear systems in the discrete-time case. The main objective consists to clarify and to correct some recent results in this field. After a state of the art, some analytic comparisons are provided. Two numerical examples are given in order to show the nonsuperiority of the result of the work of Zhang for Lipschitz nonlinearities without any additional assumption: one-sided Lipschitz and quadratically inner bounded properties.