$20$ points$)$ For each of the statement below, tell whether it is true or false. You are not expected to

explain your answers.

$($i$)$ All the roots of the polynomial s$2+9$ are in the closed right half$-$plane.

$($ii$)$ The polynomial s$3+4$s$2+5$s has a root in the open right half$-$plane.

$($iii$)$ All the roots of the polynomial s$2+$ s $+1$ are in the open left half$-$plane.

$($iv$)$ Each root locus branch starts from an open$-$loop zero and terminates at an open$-$loop pole or termi$-$

nates at infinity along an asymptote if there are not sufficient number of open$-$loop poles to terminate

all the branches.

$($v$)$ Consider the following transfer function from input U $($s$)$ to output Y $($s$)$ of a system: G$($s$)=1$

s$1.$

For a unit step input, the steady$-$state value of the output is $1.$

$($vi$)$ For a given transfer function, there is a unique state$-$space representation.

$($vii$)$ Every strictly proper transfer function is proper.

$($viii$)$ Given a transfer function with zeros, the BIBO stability is dependent on zeros.

$($ix$)$ Step responses of nonminimum phase systems can exhibit undershoot.

$($x$)$ Consider the following system

$$y $+$ y$2=$ u$,$

where y is the output and u is the input of the system. The transfer function of the system is

Y $($s$)$

U $($s$)=1$

s $+2.$