On robustness of coupled adaptive filters

We provide a time domain analysis of the robustness and stability performance for coupled adaptive algorithms of gradient type. The considered coupling may occur inherently as well as by desire of the designer. The presented analyses focus on system identification. Examples are presented to investigate convergence and steady-state behaviour by simulations which are compared to theory. In particular, the presented approach allows for a deeper understanding of cascaded adaptive filters in terms of robustness and l₂-stability.