$(2)(40$ points$)$ Oesign a Full State Feedback Controller: A second$-$ order plant is modeled by the state space equation:

$x=\left[\begin{array}{ccc}0& 16& 0\end{array}\right]$

$1^x+[10{]}^u$

$y=\left[\begin{array}{cc}11& 0\end{array}\right]x$

a$.)$ Please describe the yotem d namics. Is there anything of particular importance to be ware of for this syetem?

$$

b$.)$ Calculate the feedback gains given the desired pole placement of $p_{12}=-2+-21.$ What important characteristic of the syetem has changed with this pole placement.

Feedback Gains

What important characteristic has changed?

c$)$ Calculate the controller effort u if reference $r=0$ at some time $t$ when state values are $x=\left[\begin{array}{c}2\\ 4\end{array}\right]$