In this note, we investigate the convergence of a robust recursive identifier for linear models subject to impulsive disturbances. Under the assumption that the disturbance is unknown and can be of arbitrarily large magnitude, the analyzed algorithm attempts to minimize online the sum of absolute errors so as to achieve a sparse prediction error sequence. It is proved that the identifier converges exponentially fast into an euclidean ball whose size is determined by the richness properties of the estimation data, the frequency of occurrence of impulsive errors and the parameters of the algorithm. (C) 2016 Elsevier Ltd. All rights reserved.