Q$1(22\mathrm{.}5\%)$

An LTI system is described by the following parameters of the state$-$space model

$=[122050140]=[101]=[010]$ D $=1$

$($a$)$ Check whether system is controllable. If not, find the controllable component.

$($b$)$ Check whether system is observable. If not, find the observable component.

$($c$)$ Check whether the system is Minimal. If not, find the minimal system.

$($d$)$ Determine the dual system. Check its controllability and observability