state space control of an inverted pendulum

Hi,

I am working on an opensource project with a robot similar to the JOE le pendule:

and am trying to copy their state space control algorithm for it. I am using a PID loop for balancing right now but I would like to experiment with state space control too.

I can generate the 6 input state variables from their paper using the gyro's and the wheel encoders: "

" I am not sure how to proceed with the state space matrices to go from these variables to the required wheel torques. Thank you very much for any help on this!

best regards, Jamie Morken