Multiple choice

The signal flow graph of a system is shown below.

Which of the following is the state variable representation of the system?

  1. $ x = \left[ \begin{array} \ 1 & 1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0 & 0.5] x
  2. $ x = \left[ \begin{array} \ -1 & 1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0 & 0.5] x
  3. $ x = \left[ \begin{array} \ 1 & -1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0.5 & 0.5] x
  4. $ x = \left[ \begin{array} \ -1 & 1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0.5 & 0.5] x
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D Correct answer
Explanation

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