State Space Model in Controllable Canonical Form

Mathematica by default puts state space model realizations in controllable companion form, as seen here:

tfsys = TransferFunctionModel[(b1 s^2 + b2 s + b3)/(s^3 + a1 s^2 + 
      a2 s + a3 ), s];
StateSpaceModel[tfsys]

Which outputs a block matrix like:
$$
begin{bmatrix}0 & 1 & 0 & 0 0 & 0 & 1 & 0 -a_3 & -a_2 & -a_1 & 1 b_3 & b_2 & b_1 & 0end{bmatrix}
$$
However, I want it in controllable canonical form, which should look like:
$$
begin{bmatrix}-a_1 & -a_2 & -a_3 & 1 1 & 0 & 0 & 0 0 & 1 & 0 & 0 b_1 & b_2 & b_3 & 0end{bmatrix}
$$
StateSpaceModel offers the StateSpaceRealization option but it only has ControllableCompanion and ObservableCompanion, neither of which is what I want. Is there a simple way of getting the right state space form?