State space representation in s-domain
From visual inspection of the given block diagram, we obtain

$$\begin{bmatrix} s+a &amp; -k\\ b &amp; s+p\end{bmatrix} \begin{bmatrix} X_1 (s)\\ X_2 (s) \end{bmatrix} = \begin{bmatrix} 0\\ b\end{bmatrix} U (s)$$

which can be rewritten as follows

$$\left( s \begin{bmatrix} 1 &amp; 0\\ 0 &amp; 1\end{bmatrix} - \begin{bmatrix} -a &amp; k\\ -b &amp; -p\end{bmatrix} \right) \begin{bmatrix} X_1 (s)\\ X_2 (s) \end{bmatrix} = \begin{bmatrix} 0\\ b\end{bmatrix} U (s)$$

Hence,

$$\mathrm A := \begin{bmatrix} -a &amp; k\\ -b &amp; -p\end{bmatrix} \qquad\qquad \mathrm b := \begin{bmatrix} 0\\ b\end{bmatrix}$$

Since $Y (s) = X_1 (s)$,

$$\mathrm c^\top := \begin{bmatrix} 1 &amp; 0\end{bmatrix} \qquad\qquad d := 0$$