20. 則下列何者為可控制典型式(Controllable Canonical Form)?
(A) \( \dot{X}(t) = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -\beta_1 & -\beta_2 & -\beta_3 \end{bmatrix} X(t) + \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} U(t) \),\( Y(t) = \begin{bmatrix} \alpha_1 & \alpha_2 & \alpha_3 \end{bmatrix} X(t) \)
(B) \( \dot{X}(t) = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ \beta_3 & \beta_2 & \beta_1 \end{bmatrix} X(t) + \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} U(t) \),\( Y(t) = \begin{bmatrix} \alpha_3 & \alpha_2 & \alpha_1 \end{bmatrix} X(t) \)
(C) \( \dot{X}(t) = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -\beta_1 & -\beta_2 & -\beta_3 \end{bmatrix} X(t) + \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} U(t) \),\( Y(t) = \begin{bmatrix} \alpha_3 & \alpha_2 & \alpha_1 \end{bmatrix} X(t) \)
(D) \( \dot{X}(t) = \begin{bmatrix} 0 & 0 & -\beta_1 \\ 1 & 0 & -\beta_2 \\ 0 & 1 & -\beta_3 \end{bmatrix} X(t) + \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} U(t) \),\( Y(t) = \begin{bmatrix} \alpha_1 & \alpha_2 & \alpha_3 \end{bmatrix} X(t) \)

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