系统的传递函数为则其状态空间表达式正确的是： \(g(s)=\dfrac{s^2+3s+2}{s(s^2+7s+12)}\)
A. \( \begin{equation} \dot{x}= \left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & -4 \end{matrix} \right] x+ \left[ \begin{matrix} 0 \\ 1 \\ 1 \end{matrix} \right] u,\,\,\,\, y= \left[ \begin{matrix} \frac{1}{6} & -\frac{2}{3} & \frac{3}{2} \end{matrix} \right] x \end{equation} \)
B. \( \begin{equation} \dot{x}= \left[ \begin{matrix} 0 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & 4 \end{matrix} \right] x+ \left[ \begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right] u,\,\,\,\, y= \left[ \begin{matrix} \frac{1}{6} & -\frac{2}{3} & \frac{3}{2} \end{matrix} \right] x \end{equation} \)
C. \( \begin{equation} \dot{x}= \left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{matrix} \right] x+ \left[ \begin{matrix} 1 \\ 1 \\ 1 \end{matrix} \right] u,\,\,\,\, y= \left[ \begin{matrix} \frac{1}{6} & -\frac{2}{3} & \frac{3}{2} \end{matrix} \right] x \end{equation} \)
D. \( \begin{equation} \dot{x}= \left[ \begin{matrix} 0 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & -4 \end{matrix} \right] x+ \left[ \begin{matrix} 1 \\ 1 \\ 1 \end{matrix} \right] u,\,\,\,\, y= \left[ \begin{matrix} \frac{1}{6} & -\frac{2}{3} & \frac{3}{2} \end{matrix} \right] x \end{equation} \)
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