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The model reference adaptive system approach together with the positivity lemma for time varying discrete systems are used to construct recursive identifiers with a parallel adjustable model, using adaptation algorithms having a decreasing gain. Identification of single input-single output systems and of multivariable systems is discussed. The identifiers assure an asymptotic unbiased parameter estimation in the presence of noise obscured measurements. Experimental results obtained from simulated data and from the identification of a paper machine are presented. The comparison with the performances of other identification methods is discussed.