$28.$ A system is described using two state$-$space models as seen above. What is the correct State Transfor$-$

mation Matrix converting from the Physics$-$based to the RCF form?

$($a$)$

$($b$)$

$($c$)$

$($d$)$

$($e$)$ None of the above

$$x $=$

$[01$

$65$

$]$

x $+$

$[0$

$1$

$]$

u

y $=[81]$ x

$29.$ A system is described using the state$-$space model as seen above. Determine the gain Matrix K if the

desired closed$-$loop poles are to be at s $=10?$

$($a$)$ K $=[8042]$

$($b$)$ K $=[2900290]$

$($c$)$ K $=[0\mathrm{.}330\mathrm{.}75]$

$($d$)$ K $=[9415]$

$($e$)$ None of the above

$30.$ A system is described using the state$-$space model as seen above. Which of the following Transformation

Matrices will convert this State Space Model to the Jordan Normal Form? Note: Set the Transformation

Matrix up to have the pole with the larger absolute value first. e$.$g$.$ if the poles are $10$ and $11$ the T

matrix should be set up for $11$ to have the first eigen vector.

$7$