Question $8$

$($a$)($i$)$ What do you mean when you say that a system is stable?

$($ii$)$ What are the restrictions on the roots of the characteristic equation of a system for the system to be stable?

$($b$)$ Find the roots of the characteristic equations for the systems whose open loop

$6$

transfer functions are given below. Plot the roots on the splane for each system and indicate if each system is stable, or marginally stable or not stable.

$($i$)G(s)H(s)=\frac{1}{(s+2)(s+4)}$

$($ii$)G(s)H(s)=\frac{9}{s^2(s+2)}$

$($iii$)G(s)H(s)=\frac{1}{(s-1)(s+2)}$