The SISO system with transfer function

\[
\mathrm{T}(s)=\frac{\mathrm{Y}(s)}{\mathrm{U}(s)}=\frac{9}{(s+2)\left(s^{2}+4 s+13ight)}
\]

involves complex characteristic roots. Obtain the diagonal form of state space model. Also obtain an alternative block diagonal model which does not involve complex numbers.

Solution: Expand the transfer function in partial fractions to get