on a modified reference system given by (\[ref:nonideal\]), Theorem 5.1 shows that $\lim_{t\rightarrow\infty}\bigl(x(t)-x_\rom{r_i}(t)\bigl)=0$, that is the (augmented) state vector $x(t)$ of (\[unc:sys2\]) asymptotically converges to the ideal reference state vector $x_\rom{r_i}(t)$ of (\[ref:ideal:2\]). Furthermore, during transient time (learning phase), the worst-case transient performance bound between $x(t)$ and $x_\rom{r_i}(t)$ is given by (\[bound:1\]). To further elucidate this performance bound, we let $x_\rom{r_0}=x_0$ in (\[ref:nonideal\]), and hence, $e(0)=0$ in (\[err:sys:mod\]). As noted in Remark 3.1, since it is assumed that the state vector $x_\rom{p}(t)$ in (\[unc:sys\]) is accessible, this condition is realizable \[, Section II.C\]. Now, denoting $\epsilon_{\mathcal{V}_1}\triangleq \norm{\tilde{W}_0\Lambda^\frac{1}{2}}_\rom{F}/\sqrt{\lambda_\rom{min}(P)}$ and $\epsilon_{\mathcal{V}_2}\triangleq \sqrt{  \frac{1}{2}\xi^{-1}\lambda_\rom{min}^{-1}(R)\lambda_\rom{min}(P)  }$, it follows from (\[bound:1\]) that \_[\_]{}\^[-]{}\_[\_1]{}(1+\^\_[\_2]{}), \[bound:elu\] for all $t \in \overline{\IR}_+$. The performance bound in (\[bound:elu\]) implies that the distance between $x(t)$ and $x_\rom{r_i}(t)$ can be made arbitrarily small in transient time by resorting to a high learning rate $\gamma$, similar to Remark 3.1 for the standard model reference adaptive control scheme. However, as we see in the next section, by increasing $\kappa$, we make the distance between $e(t)$ and $e_\rom{L}(t)$ sufficiently small in transient time, and hence, a high learning rate $\gamma$ subject to a high $\kappa$ does not yield to signals with high-frequency oscillations. Finally, 