How to find the state-variable equations from the signal flow graph of the system?
Between each point you have to define a state-variable and it will give you this equations:

$$
\begin{align}
&amp; X_1 = U \\
&amp; X_2 = -X_1 \\
&amp; X_1(point)=X_2 \\
&amp; X_2 = -X_1 \\
&amp; X_2(point) = X_3 \\
&amp; X_3 = -X_2 \\
&amp; X_3(point) = -X_3 \\
&amp; Y = X_3 \\
\end{align}
$$

$$
X(point) = \begin{bmatrix}0 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 1 \\ 0 &amp; 0 &amp; -1\end{bmatrix}*X \\
Y= \begin{bmatrix}0 &amp; 0 &amp; 1\end{bmatrix}X 
$$
For example you have \$ X_3 (t) = C_0 \cdot ^{(-t)} \$ (if you solve this equation).