Averaging matrix is not invertible in state space averaging
How can this work? I don't see-it anywhere but this should be a DC converter ? There is no DC path to Vo1 and Vo2, the average will always be zero. Are you sure Cf1 and Cf2 are in the right place? Switching to the configuration in Page 2 is not possible, it will lead to infinite current since on the Vin - Cf1 - C1 loop there are no resistive or inductive loads. Also on Vin - Cf1 - C1 loop. It's not about the efficiency, revise the structure of the converter, it cannot work, no wonder it's not solvable.