S F L

160 Wellposedness of the SFL

The standard form of the rational simple feedback loop linear system has inputs $r, d$ and $n$ and states $x, y$ and $z$ so that

x=r-z

y=d+Kx

z=n+Gy

for some rational functions $G$ and $K$ , hence

\begin{bmatrix}1&0&1\\ -K&1&0\\ 0&-G&1\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}=\begin{bmatrix}r\\ d\\ n\end{bmatrix}.

Definition (Well posed)

The system is said to be well posed if the inputs $(r,d,n)$ uniquely determine the states $(x,y,z)$ .