Write an IIR (or ARMA) model in state space representation:
[tex]y(k) = b_1 y(k-1) + \cdots + b_p y(k-p) + a_0 u(k) + \cdots + a_r u(k-r)[/tex]
The Attempt at a Solution
I found much info how to write it in space state representation but no explanation how to get there. The main problem is how to choose the state vector and how to derive the transition matrix.
For a AR and MA only system, I found the solution (I think): The state vector is just u(k)'s or the y(k)'s: It's just the equation given. Then I used "k+1" instead of "k" in the argument and found that the transition matrix must be the identify matrix.
Can anyone tell me what the "steps" are required to get there? I am confused since I only have one equation given, but I need to come up with two equations ...