  In this letter, we analyze, two properties, the local and the global
robustness of the set-membership normalized least mean square (SM-NLMS)
algorithm. We will show that the SM-NLMS algorithm has l2-stability. Indeed,
the SM-NLMS algorithm never diverges; no matter how the parameters of the
SM-NLMS algorithm has been selected. Ultimately, the numerical simulations
corroborate the validity of our analysis.
