A system using state feedback control is governed by the following set of equations. Determine feedback gains so as to place the closed loop system poles at \(s=-4\) and \(-4 \pm j 2\).

\[
\begin{aligned}
{\left[\begin{array}{l}
\dot{x}_{1} \\
\dot{x}_{2} \\
\dot{x}_{3}
\end{array}ight] } & =\left[\begin{array}{rrr}
0 & 0 & 1 \\
3 & -2 & -1 \\
0 & 1 & 0
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2} \\
x_{3}
\end{array}ight]+\left[\begin{array}{rr}
0 & -1 \\
1 & 0 \\
0 & 1
\end{array}ight]\left[\begin{array}{l}
r \\
u
\end{array}ight] \\
y & =-\left[\begin{array}{lll}
\mathrm{K}_{1} & \mathrm{~K}_{2} & \mathrm{~K}_{3}
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2} \\
x_{3}
\end{array}ight] \\
y & =\left[\begin{array}{lll}
1 & 0 & 0
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2} \\
x_{3}
\end{array}ight]
\end{aligned}
\]