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Consider the state space model of a system, as given below

$\begin{bmatrix} x_{1}\\x_{2} \\x_{3} \end{bmatrix} \begin{bmatrix} -1 &1 &0 \\ 0& -1 &0 \\ 0 & 0 & -2 \end{bmatrix}\begin{bmatrix} x_{1}\\x_{2} \\x_{3} \end{bmatrix} + \begin{bmatrix} 0\\4 \\0 \end{bmatrix} u;\:\: y = \begin{bmatrix}1 & 1&1 \end{bmatrix} \begin{bmatrix} x_{1}\\x_{2} \\x_{3} \end{bmatrix} $

The system is

  1. controllable and observable
  2. uncontrollable and observable
  3. uncontrollable and unobservable
  4. controllable and unobservable
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