Stationary behavior of an anti-windup scheme for recursive parameter estimation under lack of excitation

Stationary properties of a recently suggested windup prevention scheme for recursive parameter estimation are investigated in the case of insufficient excitation. When the regressor vector contains data covering the whole parameter space, the algorithm has only one stationary point, the one defined by a weighting matrix. If the excitation is insufficient, the algorithm is shown to possess a manifold of stationary points and a complete parametrization of this manifold is given. However, if the past excitation conditions already caused the algorithm to converge to a certain point, the stationary solution would not be affected by current lack of excitation. This property guarantees good anti-windup properties of the studied parameter estimation algorithm.