Consider the continuous-time system:
\frac{d\mathbf{x}}{dt} = \begin{bmatrix} -1 & -2\2 & -1\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\1\end{bmatrix} u(t),\qquad y(t) = \begin{bmatrix} 1 & 0\end{bmatrix}\mathbf{x}(t)
Which of the following is true?

Question

Consider the continuous-time system:  
  \frac{d\mathbf{x}}{dt} = \begin{bmatrix} -1 & -2\2 & -1\end{bmatrix}\mathbf{x}(t) + \begin{bmatrix} 1\1\end{bmatrix} u(t),\qquad y(t) = \begin{bmatrix} 1 & 0\end{bmatrix}\mathbf{x}(t) 
 Which of the following is true?

Accepted Answer

The eigenvalues are   -1 + 2j  and   -1-2j  and the system is internally stable.

Answer

The eigenvalues are   -3  and   1  and the system is not internally stable.

Answer

The eigenvalues are   1 + 2j  and   1-2j  and the system is not internally stable.

Answer

The eigenvalues are   -1 + 2j  and   -1-2j  and the system is not internally stable.

Crowdly

Consider the continuous-time system: \frac{d\mathbf{x}}{dt} = \begin{bmatrix...

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