For given the system represented in state space,

$\left[\begin{array}{c}{x}_1^{}\\ x_2^{}\\ x_3^{}\end{array}\right]=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ -24& -26& -9\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ x_3\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]e^{-t},x(0)=\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]$

$(1)$ Obtain the states $x_1(s),x_2(s),x_3(s)$ on frequency domain using Laplace transformation.

$(2)$ For given the unit feedback system with $x_2(s)$ which is obtained from $(1),$

Find the value of $K$ so that there is steady$-$state erron $3$ on closed$-$loop system.