$4\mathrm{.}44$ An unstable LTI system has the impulse response

h$($t$)=$ e$3$t u$($t$)$e$2$t u$($t$).$

$($a$)$ Show that proportional feedback $($using G$($s$)=$ K$)$

cannot BIBO$-$stabilize the system.

$($b$)$ Show that derivative feedback $($G$($s$)=$ Ks$)$ can stabilize

the system, but the closed$-$loop system has a pole

p $6,$ so its step response is slow.

$($c$)$ Show that proportional$-$plus$-$derivative feedback control,

$($G$($s$)=$ K$1+$K$2$s$),$ can be used to put both closed$-$loop

poles at $10.$ Compute K$1$ and K$2$ to accomplish this.