In this paper, we derive two robustness properties for the set-membership normalized least-mean-square (SM-NLMS) algorithm. The first property provides local bounds for the error/discrepancy in the coefficient vector at a given iteration, whereas the second property expands the previous one for any given iteration. As a result, this paper demonstrates for the first time that the SM-NLMS algorithm is robust (1 2 -stable), no matter how the algorithm parameters are set.
['Hamed Yazdanpanah', 'Markus V. S. Lima', 'Paulo S. R. Diniz']
On the robustness of the set-membership NLMS algorithm