state-space averaging with matrices not same dimension
Try this for state 1:

$$\pmatrix{\frac{di_L}{dt}\\\frac{dv_{c1}}{dt}\\\frac{dv_{c2}}{dt}} = \pmatrix{a_{11} &amp; a_{12} &amp; 0\\a_{21} &amp; a_{22} &amp; 0 \\ 0 &amp; 0 &amp; 0} \pmatrix{i_L \\ v_{c1} \\ v_{c2}}$$

As you can see from the A matrix, \$v_{c2}\$ makes no contribution to any of the equations, and also the derivative \$\frac{dv_{c2}}{dt}\$ will always be zero which makes sense as \$v_{c2}\$ is always zero.

I'm not saying that this is the correct derivation: it seems to me from the circuit that the voltage over C2 will change and therefore you need terms to account for this, but purely from the standpoint of making the matrices the same size, this is how you would accomplish that.