I have a stochastic MIMO state space system as follows: \begin{align*} x_{k+1} &= Ax_k + w_k\\ y_k &= Cx_k + v_k \end{align*}
I want to find the transformation matrix $T$ for converting $A$ to observable canonical form $A_o$ using relation \begin{equation*} A_o = T^{-1} A T \end{equation*} and with that, $C$ gets transformed to $C_o = CT$. I tried using MATLAB canon function, but it needs the knowledge of $B$ matrix. If $B$ is set to zero matrix then canon throws out an error. Is there any way to get the transformation matrix $T$ without the need for matrix $B$?
Any reference would be greatly appreciated. Thanks!