state-space model for bidirectional buck-boost with input capacitors
Consider the output \$y(t)\$, as typically represented in state-space models: \$y(t) = Cx(t)+Du(t)\$. If you were to equate one element of \$x(t)\$ to \$u(t)\$, then this means the original representation was incorrect in the first place, and rather a representation \$y(t) = \tilde{C}\tilde{x}(t)+\tilde{D}u(t)\$ was the correct one. Demonstration: if state \$x_3\$ is equal to \$u\$:

$$
y(t) = Cx(t)+Du(t) = \begin{bmatrix}c1&amp;c2&amp;c3\end{bmatrix}\begin{bmatrix}x_1(t)\\x_2(t)\\u(t)\end{bmatrix}+[d_1]u(t) \\
= \begin{bmatrix}c1&amp;c2\end{bmatrix}\begin{bmatrix}x_1(t)\\x_2(t)\end{bmatrix}+[c_3+d_1]u(t) = \tilde{C}\tilde{x}(t) + \tilde{D}u(t)
$$

This serves to show that if a system variable is equal to an exogenous signal, then this is not an internal system variable. To consider the voltage over C1 as state variable would be incorrect.