How to model state space for complex valued system correctly in SIMULINK (MATLAB)?
You can split up the real and imaginary part of the state into their own seperate states. Namely by defining $x_r=\mathrm{Re}(x)$, $x_i=\mathrm{Im}(x)$, $A_r=\mathrm{Re}(A)$, $A_i=\mathrm{Im}(A)$, $u_r=\mathrm{Re}(u)$, $u_i=\mathrm{Im}(u)$, $B_r=\mathrm{Re}(B)$ and $B_i=\mathrm{Im}(B)$ then the differential equation can also be written as

$$
\dot{x}_r+i\,\dot{x}_i=(A_r+i\,A_i)(x_r+i\,x_i)+(B_r+i\,B_i)(u_r+i\,u_i)
$$

which when split into their real and imaginary part gives

$$
\begin{bmatrix}
\dot{x}_r \\ \dot{x}_i
\end{bmatrix}=
\begin{bmatrix}
A_r &amp; -A_i \\
A_i &amp; A_r
\end{bmatrix}
\begin{bmatrix}
x_r \\ x_i
\end{bmatrix}+
\begin{bmatrix}
B_r &amp; -B_i \\
B_i &amp; B_r
\end{bmatrix}
\begin{bmatrix}
u_r \\ u_i
\end{bmatrix}.
$$

The output can be expressed using

$$
y=C\begin{bmatrix}
I &amp; i\,I
\end{bmatrix}
\begin{bmatrix}
x_r \\ x_i
\end{bmatrix} + D\begin{bmatrix}
I &amp; i\,I
\end{bmatrix}
\begin{bmatrix}
u_r \\ u_i
\end{bmatrix}.
$$