State Space Model for an eletronic circuit

Hello!

I am trying to find a space state model for the following circuit. :


My approach was trying to divide the circuit in various blocks and then find the output expression for those blocks.

So i have defined the voltages Vout1,Vout2 has shown in the circuit.

Then i have calculated the ouput expressions for the blocks i have considered and i got:






For this block i wrote the following set of equations in order to find an expression in order to vout2:



So the matrix that represent the space state model of the circuit in the form



So considering the above form i got the following matrix and equations:




Is this correct? Thanks