Question $11$

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Determine the state$-$space model of the system given by the following transfer function:

$\frac{Y(s)}{U(s)}=\frac{6}{3s^2-12s+18}$

a$.$

$\left[\begin{array}{c}{x}_1^{}\end{array}\right]$

$x_2^{}=\left[\begin{array}{ccc}0& 1& 4\end{array}\right]$

$-6*\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2$

$y=\left[\begin{array}{cc}1& 0\end{array}\right]*\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2+[0]*u$

b$.$ None of these

c$.\left[\begin{array}{c}{x}_1^{}\\ x_2^{}\end{array}\right]=\left[\begin{array}{cc}0& 1\\ -6& 4\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]$

$y=\left[\begin{array}{cc}0& 1\end{array}\right]*\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+[0]*u$

d$.$

$\left[\begin{array}{c}{x}_1^{}\end{array}\right]$

$x_2^{}=\left[\begin{array}{ccc}0& 1& -4\end{array}\right]$

$6*\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2$

$y=\left[\begin{array}{cc}1& 0\end{array}\right]*\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2+[0]*u$

e$.$

$\left[\begin{array}{c}{x}_1^{}\end{array}\right]$

$x_2^{}=\left[\begin{array}{ccc}0& 1& -4\end{array}\right]$

$6*\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2$

$y=\left[\begin{array}{cc}1& 0\end{array}\right]*\left[\begin{array}{c}{x}_1\end{array}\right]$

$x_2+[0]*u$

Question $11$

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Determine the state$-$space model of the system given by the following transfer function:

$\frac{Y(s)}{U(s)}=\frac{6}{3s^2-12s+18}$

$[$:$[],[2]$