This is a kalmanfilter
As you can see, the process noise(disturbance) is not going to the kalmanfilter. But the state space model for the state feedback system is written as this: https://youtu.be/H4_hFazBGxU?t=5m43s
So what is right and what is wrong? Should a kalmanfilter have disturbance as input too?
Like this. With disturbance as input:
$$ \ \begin{bmatrix} \dot{x} \\ \\\dot{\tilde{x}} \end{bmatrix} =\begin{bmatrix} A - BL& BL \\ 0 & A-KC \end{bmatrix} \begin{bmatrix} x\\ \tilde{x} \end{bmatrix}+\begin{bmatrix} I & 0\\ I & K \end{bmatrix}\begin{bmatrix} d\\ n \end{bmatrix}\ $$
Or this. Without disturbance as input:
$$ \ \begin{bmatrix} \dot{x} \\ \\\dot{\tilde{x}} \end{bmatrix} =\begin{bmatrix} A - BL& BL \\ 0 & A-KC \end{bmatrix} \begin{bmatrix} x\\ \tilde{x} \end{bmatrix}+\begin{bmatrix} I & 0\\ 0 & K \end{bmatrix}\begin{bmatrix} d\\ n \end{bmatrix}\ $$