H/sup /spl infin// bounds for the recursive-least-squares algorithm

We obtain upper and lower bounds for the H/sup /spl infin// norm of the RLS (recursive-least-squares) algorithm. The H/sup /spl infin// norm may be regarded as the worst-case energy gain from the disturbances to the prediction errors, and is therefore a measure of the robustness of an algorithm to perturbations and model uncertainty. Our results allow one to compare the robustness of RLS compared to the LMS (least-mean-squares) algorithm, which is known to minimize the H/sup /spl infin// norm. Simulations are presented to show the behaviour of RLS relative to these bounds.<
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