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\textbf{1. Considering $k\neq 0$, what is the relative degree n^∗ of the plant?}  The relative degree is defined as the difference between the degree of the denominator's polynomial order and the numerator's polynomial order. Given Figure figure  (\ref{fig:plant}) we determine the transfer function $G_{nm}$ as follows. \begin{equation}G_{nm}=\frac{k+\theta_u^TF}{s-a-\theta_y^TF}=\frac{\lambda k+\theta_u^T\xi}{\lambda s-\lambda a-\theta_a^T\xi}\end{equation}  Since $\lambda$ is given to be of degree $n-1$, the numerator's polynomial has degree $n-1$ while the denominator's polynomial has degree $n$. Therefore the relative degree equals one.