Consider the system defined by
\frac{d\mathbf{x}}{dt} = \begin{bmatrix} 2 & 1\1 & 0\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\0\end{bmatrix}u(t)\quad extrm{and}\quad y(t) = \begin{bmatrix} 1 & 0\end{bmatrix}\mathbf{x}(t).
Which of the following statements is true?

Question

Consider the system defined by 
  \frac{d\mathbf{x}}{dt} = \begin{bmatrix} 2 & 1\1 & 0\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\0\end{bmatrix}u(t)\quad	extrm{and}\quad y(t) = \begin{bmatrix} 1 & 0\end{bmatrix}\mathbf{x}(t). 
 Which of the following statements is true?

Answer

If output feedback is used, it is not possible to choose observer feedback gains   \mathbf{L}  and state feedback gains   \mathbf{K}  so that   \mathbf{A} - \mathbf{B}\mathbf{K}  and   \mathbf{A} - \mathbf{L}\mathbf{C}  have eigenvalues in any desired locations.

Answer

If output feedback is used, it is possible to choose observer feedback gains   \mathbf{L}  and state feedback gains   \mathbf{K}  so that   \mathbf{A} - \mathbf{B}\mathbf{K}  and   \mathbf{A} - \mathbf{L}\mathbf{C}  have eigenvalues in any desired locations.

Crowdly

Consider the system defined by \frac{d\mathbf{x}}{dt} = \begin{bmatrix} 2 & 1...

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