Exponential convergence of recursive least squares with exponential forgetting factor

This paper demonstrates that, provided the system input is persistently exciting, the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent. Further, it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary. The result holds for stable finite-dimensional, linear, time-invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail.