The state-space representation in phase-variable form for the transfer function [ G(s)=frac{2 s+1}{s^{2}+7 s+9} quad text {
Question:
The state-space representation in phase-variable form for the transfer function
\[
G(s)=\frac{2 s+1}{s^{2}+7 s+9} \quad \text { is }
\]
(a) \(\dot{x}=\left[\begin{array}{rr}0 & 1 \\ -9 & -7\end{array}ight] x+\left[\begin{array}{l}0 \\ 1\end{array}ight] u: y=\left[\begin{array}{ll}1 & 2\end{array}ight] x\)
(b) \(\dot{x}=\left[\begin{array}{rr}0 & 1 \\ -9 & -7\end{array}ight] x+\left[\begin{array}{l}0 \\ 1\end{array}ight] u: y=\left[\begin{array}{ll}0 & 1\end{array}ight] x\)
(c) \(\dot{x}=\left[\begin{array}{rr}-9 & 0 \\ 0 & -7\end{array}ight] x+\left[\begin{array}{l}0 \\ 1\end{array}ight] u: y=\left[\begin{array}{ll}2 & 0\end{array}ight] x\)
(d) \(\dot{x}=\left[\begin{array}{rr}9 & -7 \\ 1 & 0\end{array}ight] x+\left[\begin{array}{l}0 \\ 1\end{array}ight] u: y=\left[\begin{array}{ll}1 & 2\end{array}ight] x\)
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