Consider the system described by the transfer function

$2$

$2$

$()0\mathrm{.}9$

$()()1\mathrm{.}50\mathrm{.}5$

Y z z z

G z U z z z

$+$

$==+$

$($a$)$ Find two different state space representation for G$($z$).$

$($b$)$ Find the state transition matrix $($k$)$ for this system