From idpoly to ss : why, with the ss command, do i not get always the same state space convention ?

Hello,

From CFD simulations, I perform system identification. I get a model which link my output y to my input u. It is an idpoly, variable z (time discrete). So the idpoly.B matrix contains all the coefficients of my unit impulse response.

From that, I want to transform it to state space representation. Straight forward with the command ss. But, for one transfer function, there is not a unique state space description.

Most of the time I get this state space with , and C and D having the coefficients of my Unit Impulse Response (U.I.R), so and

But sometimes, Matlab will give me a different convention ; A doesn't change but , alpha being an integer different from 1, and therefore C changes accordingly .

I agree that this is just a matter of convention of your state vector, that the state space describes the exact same system. But in my application, I need to be sure that the C matrix contains exactly the coefficients of my U.I.R and not scaled by this alpha factor.

I did not find any options in the ss command to force that.

I could do it manually with a if loop. But i was wondering, why is Matlab sometimes changing these B&C matrices ? Is there a way to make the ss command give always the same result?

Thanks in advance