approximately recover the ideal (unmodified) reference system given by (\[ref:ideal\]). In this case, the proposed approach converges to a standard model reference adaptive control scheme, which has practical limitations as discussed earlier in the presence of high learning rate $\gamma$. Furthermore, as a special case of $\eta=0$, the proposed approach converges to the approach documented in [@notable:3], since $e_\rom{L}(t)\equiv0$ for all $t \in \overline{\IR}_+$ as a consequence of (\[filter\]). Once again, as discussed earlier, this selection for the filter gain $\eta$ may result in poor transient performance in the presence of exogenous low-frequency persistent disturbances. Therefore, from a practical point of view, this imposes another constraint in the selection of filter gain such that it also needs to satisfy $\eta_*\le\eta$, where $\eta_*\in\IR_+$ needs to be large enough in order to suppress the effects of exogenous low-frequency persistent disturbances. This phenomenon is illustrated in the next remark for a special case as well as later in the paper for a more general case.

*Remark 4.3*. To further elucidate the mechanism behind the proposed approach, let $n_\rom{p}=1$, $n_\rom{c}=0$, $m=1$, $A_\rom{p}=-\alpha$, $\alpha\in\IR_+$, $B_\rom{p}=\alpha$, $K=0$, and $\delta_\rom{p}\bigl(x_\rom{p}\bigl)=d$ with $d$ denoting an exogenous low-frequency disturbance. Furthermore, set $R=2$ in (\[lyap:eqn\]) such that $P=\alpha^{-1}$ and let 