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The state diagram of a system is shown below. A system is described by the state-variable equations

$$\dot{X}= AX+Bu;\:\: y = CX+Du$$

The state-variable equations of the system shown in the figure above are

  1. $\dot{X} = \begin{bmatrix} -1 & 0 \\ 1 & -1 \end{bmatrix}X + \begin{bmatrix} -1\\ 1 \end{bmatrix}u\:,\:\:\:\:y =\begin{bmatrix} 1&-1 \end{bmatrix}X + u$
  2. $\dot{X} = \begin{bmatrix} -1 & 0 \\ -1 & -1 \end{bmatrix}X + \begin{bmatrix} -1\\ 1 \end{bmatrix}u\:,\:\:\:\:y =\begin{bmatrix} -1& -1 \end{bmatrix}X + u$
  3. $\dot{X} = \begin{bmatrix} -1 & 0 \\ -1 & -1 \end{bmatrix}X + \begin{bmatrix} -1\\ 1 \end{bmatrix}u\:,\:\:\:\:y =\begin{bmatrix} -1& -1 \end{bmatrix}X - u$
  4. $\dot{X} = \begin{bmatrix} -1 & -1 \\ 0 & -1 \end{bmatrix}X + \begin{bmatrix} -1\\ 1 \end{bmatrix}u\:,\:\:\:\:y =\begin{bmatrix} 1& -1 \end{bmatrix}X - u$
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