Necessary and sufficient condition on convergence and robustness for a class of iterative algorithms with applications in adaptive filtering

The following class of recursive algorithm is considered: [X _n+1=X_n+a_n (B +C_n)X_n+b_n ]. Under weaker assumptions about {C_n} than those used for previous results, the necessary and sufficient condition on {b_n} for the convergence of this algorithm is established, and its robustness is examined. These results are then applied to an adaptive filtering algorithm in order to obtain better convergence and robustness results than those previously given by the authors (1991)