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\section{System analysis}  \textbf{ 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 numerator's polynomial order and the denominator's polynomial order. In order to determine the relative degree of the system the transfer function $G_{nm}$ has to be evaluated.   \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  relative degree 1  order of $G_nm = n$