Q$2$: Consider the system with the transfer function $(40$ points$)$

n a$.$ Find the observer canonical form $($A o$,$B o$,$C o$)$

n b$.$ Is $($A o$,$B o$)$ controllable?

n c$.$ Computer K so the closed$-$loop poles are $=33,$ using the observer

canonical form from $($a$).$

n d$.$ Is the closed$-$loop system of $($c$)$ observable?

n e$.$ For the original system, design a full$-$order estimator with estimator error

poles $=1212$

n f$.$ Suppose the system is modified as $=0(23$$$)$

$2!$ #$0.$ Under the observer

canonical form, prove if $=+,$ there is a feedback gain K that can

make the closed$-$loop system unobservable.