hence, to filter out any possible high-frequency oscillations contained in the error signal $e(t)$. For this purpose, let $e_\rom{L}(t) \in \IR^n$ be a low-pass filtered system error of $e(t)$ given by \_(t)&=&A\_e\_(t)+(e(t)-e\_(t)), e\_(0)=0, \[filter\]      where $\eta\in\IR_+$ is a filter gain. Note that since $e_\rom{L}(t)$ is a low-pass filtered system error of $e(t)$, the filter gain $\eta$ is chosen such that $\eta\le\eta^*$, where $\eta^*\in\IR_+$ is a design parameter.

Next, we add a mismatch term to the system error dynamics (\[err:sys\]) in order to enforce a distance condition between the trajectories of the system error $e(t)$ and the trajectories of its low-pass filtered version $e_\rom{L}(t)$. This leads to a minimization problem involving an error criterion capturing the distance between $e(t)$ and $e_\rom{L}(t)$. In particular, consider the cost function given by (e,e\_) &=& \_2\^2, \[cost:func\] and note that the negative gradient of (\[cost:func\]) with respect to $e$ is given by =-(e(t)-e\_(t)), \[deriv:cost\] which gives the structure of the proposed mismatch term. Using the idea presented in \[,–\], we now need to add (\[deriv:cost\]) to the system error dynamics given by (\[err:sys\]). For this purpose, we modify the reference system (\[ref:ideal\]) as \_(t)&=&A\_x\_(t)+B\_c(t)+(e(t)-e\_(t)), x\_(0)=x\_, \[ref:nonideal\] where $\kappa\in\IR_+$, and hence, the system error dynamics is 