I am trying to generate the state space model for the following system:
However, the following code does not generate the state space model I expect:
tf = TransferFunctionModel[{{1/s}, {1/(s + 2)}}, s]
ssm = StateSpaceModel[tf]
What I'm expecting is
$A = \begin{bmatrix} -2 & 0 \\ 1 & 0 \end{bmatrix}$ $B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$ $C = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ $D = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$
but what I'm getting is
$A = \begin{bmatrix} 0 & 1 \\ 0 & -2 \end{bmatrix}$ $B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$ $C = \begin{bmatrix} 2 & 1 \\ 0 & 1 \end{bmatrix}$ $D = \begin{bmatrix} 0 \\ 0 \end{bmatrix}$
The state equations are:
$$\dot{x_1}(t) = -2 x_1 (t) + w_1 (t) $$ $$\dot{x_2}(t) = x_1(t) + u(t)$$ $$y_1(t) = x_2(t)$$ $$y_2(t) = \dot{x}_2(t)$$
where $w_1(t)$ denotes the white noise added to the system, and $x_2(t)$ denotes the system error, $e$.
How should I enter my transfer function model to generate such a state space model?