State Model Representation of RLC network
You will need 4 variables and there are 4 equations

$$V_{\text{C1}}-V_{\text{C2}}=L_4 i_1'$$
$$i_1=\frac{V_i-V_{\text{C1}}}{R_2}-C_3 V_{\text{C1}}'$$
$$i_1=C_4 \left(V_0'-V_{\text{C2}}'\right)+\frac{V_{\text{C2}}}{R_5}$$
$$\frac{V_{\text{C2}}-2 V_0}{R_6}=C_4 V_0'$$

And there are 4 unknowns \$\{i_1',V_{\text{C1}}',V_{\text{C2}}',V_0'\}\$ from which you can solve for the \$A\$ and \$B\$ matrices.

$$ A=\left(
\begin{array}{cccc}
 0 &amp; \frac{1}{L_4} &amp; -\frac{1}{L_4} &amp; 0 \\
 -\frac{1}{C_3} &amp; -\frac{1}{C_3 R_2} &amp; 0 &amp; 0 \\
 -\frac{1}{C_4} &amp; 0 &amp; -\frac{-R_5-R_6}{C_4 R_5 R_6} &amp; -\frac{2}{C_4 R_6} \\
 0 &amp; 0 &amp; \frac{1}{C_4 R_6} &amp; -\frac{2}{C_4 R_6} \\
\end{array}
\right),B=\left(
\begin{array}{c}
 0 \\
 \frac{1}{C_3 R_2} \\
 0 \\
 0 \\
\end{array}
\right)
$$

I am also attaching the computations in Mathematica