L2-Stability Analysis of the SM-NLMS Algorithm

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.