linear single-track steering model. Both systems were initially given in continuous time and hence discretized by means of a Tustin approximation with a sampling time of $\SI{1}{\second}$.

### System 1

Consider a rotatory mass-spring-damper system modeled by the discrete-time second order linear state space representation $$\begin{aligned}
\label{sys_diskret}
{\boldsymbol{x}}_{k+1}={\begin{bmatrix*}[c]0.99&0.9\\-0.02&0.8
\end{bmatrix*}}{\boldsymbol{x}}_k+{\begin{bmatrix*}[c]0.01\\0.02
\end{bmatrix*}}u_k.\end{aligned}$$

The control input $u_k$ is a torque command applied to the system. Note that this system is not known to the controller and only needed for simulation as well as validation purposes. Furthermore, let $$\begin{aligned}
{\boldsymbol{Q}}=\text{diag}(100, 0) \text{ and } {\boldsymbol{R}}=1\end{aligned}$$ be the parameters of the cost function , i.e. we focus on tracking a reference angle $x_{1,\text{ref}}=\alpha_\text{ref}$ that is given on a moving horizon of length $N=10$.

### System 2

Our second example system is a sixth order linear single-track steering model $$\label{continuous_ss}
{\boldsymbol{x}}_{k+1} = {{\boldsymbol{A}}}{\boldsymbol{x}}_k + {{\boldsymbol{B}}}u_k$$ with $$\setlength{\arraycolsep}{3pt}
{{\boldsymbol{A}}} = \begin{bmatrix*}[r]
-0.741          &-0.033 &0      &0  &-\SI{2.0E-4}{} &-\SI{6.4E-3}{}\\
4.146   &-0.914 &0      &0  &\SI{4.7E-3}{}  &0.151\\
2.073                               &0.043              &1      &0  &\SI{2.4E-3}{}  &0.076\\
23.326                          &0.106                                          &20 &1  &0.022  &0.693\\
23.499      &-2.593     &0      &0  &-0.939 &-2.053\\
11.749                              &-1.297                                         &0      &0  &0.031  &-0.027
\end{bmatrix*}$$ and $$\begin{aligned}
\setlength{\arraycolsep}{3pt}
{{\boldsymbol{B}}} = \begin{bmatrix}
-\SI{3.8E-4}{} & 0.0091 & 0.0046 & 0.041 & 0.117  & 0.059
\end{bmatrix}^\intercal,\end{aligned}$$ where 