On Preserving-Excitation Properties of Kreisselmeier’s Regressor Extension Scheme

In this article, we consider the excitation preservation problem of Kreisselmeier’s regressor extension scheme. We analyze this problem within the context of the dynamic regressor extension and mixing procedure. The well-known qualitative result is that such a scheme preserves excitation. We perform a quantitative analysis and derive lower bounds on the resulting regressor signal considering both persistent and interval excitation cases. We also show that the resulting signal is excited if and only if the original regressor is. Studying the dynamics of the novel regressor, we provide a lower bound on its derivative. Illustrative simulations support our theoretical results.