Convergence Analysis of Recursive Least Squares for Identifying Higher-Order Input-Output Models

When the order of the identified input-output model is higher than the true system, the regressor of recursive least squares is not persistently exciting, and standard convergence guarantees do not apply. This work analyzes the convergence of the identified model in this case, showing that it converges to the higher-order model equivalent to the true system that minimizes the regularization term.