## Stability Analysis of Oja-RLS Learning Rule

It is shown that the discrete time dynamical system defined by the Oja-RLS algorithm is stable in the closed ring K(0,9/8) – \$\\textbackslash\overline\K\\$ (0,8/9) if only the initial gain β0 is bounded by (2B) −1 , where B = b 2 and b is the bound for the learning sequence. It is rigorously proved that automatically computed gains βn in Oja-RLS scheme converge to zero with the rate 1/n, almost surely.