62 Example of realising a proper rational function by a SISO

Example

To realise

T(s)={{2s^{2}+3s+1}\over{s^{3}+6s^{2}+8s-2}}

as the transfer function of a SISO. As in Proposition 57 we introduce

A=\begin{bmatrix}0&1&0\\ 0&0&1\\ 2&-8&-6\end{bmatrix},B=\begin{bmatrix}0\\ 0\\ 1\end{bmatrix},C=\begin{bmatrix}1&3&2\end{bmatrix},D=0.

which can be realised as a feedback linear system without differentiators. In MATLAB, or similar, one can check that $T(s)=C(sI-A)^{-1}B$ .