QUESTION $8$

A closed$-$loop negative unity feedback system is used to control a system whose loop transfer function is:

$G_{c}G(s)=\frac{K(s+1)}{s(s-1)(s+4)}$

$($a$)$ Determine the range of K for stability.

$[5$ marks$]$

$($b$)$ Sketch the root locus.

$[10$ marks$]$

$($c$)$ Determine the maximum $$ of the stable complex roots.

$[5$ marks$]$