On preserving-excitation properties of a dynamic regressor extension scheme

Abstract : In this work, we consider the excitation preservation problem within the context of the Dynamic Regressor Extension and Mixing procedure. To ensure that the input excitation is not lost, we apply the Kreisselmeier’s regressor extension scheme and prove that this choice always preserves both the persistent and the interval input excitations. We also provide a lower bound on the resulting excitation level and study the dynamics of the novel regressor. Illustrative simulations support our theoretical results