Given the following open$-$loop system

$G(s)=\frac{4(s+1)}{s(s+5)(s+11)}$

design a feedback controller $u=-Kx$ where $K=\left[\begin{array}{ccc}{K}_1& K_2& K_3\end{array}\right]$ to yield a desired characteristic equation

$s^3+23s^2+101s+230=0$

$($a$)$ Find $K_1,K_2,$ and $K_3$ using pole placement method.

$($b$)$ With the designed controller $u=-Kx,$ find the closed$-$loop system in statespace formulation

$($c$)$ Find the transfer function of the closed$-$loop system with the design controller $u=-Kx$