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
- controllable and observable
- uncontrollable and observable
- uncontrollable and unobservable
- controllable and unobservable