Problem $2$

Consider a system modeled by the following block diagram, where A$,$B$,$cdots are the transfer

functions of the subsystems that make up the overall system:

$($a$)$ Find the transfer function of the overall system. $($Note: you do not need to simplify

any resulting fractions.$)$

$($b$)$ Suppose that A$=$B$=$F$=0,$D$=$E$=1,$C$=($K$)/($s$+2),$ where K is an adjustable constant.

Find the range of K such that the overall system is BIBO stable.

$($c$)$ Suppose now instead that, after plugging in all the values, the overall transfer

function simplifies to H$($s$)=(2)/($s$+3).$ Find the zero$-$state response of the system y$($t$)$ if

the input is x$($t$)=3$u$($t$-2)+$e$^(-$t$+5)$u$($t$-4).$