| Line 3: | Line 3: | ||
P1. | P1. | ||
| − | a) C= | + | <math>\mathbf{a)} \qquad C=\begin{bmatrix} |
| − | B & AB\end{ | + | B & AB\end{bmatrix}=\begin{bmatrix} |
1 & -1 \\ | 1 & -1 \\ | ||
-3 & 3 | -3 & 3 | ||
| − | \end{ | + | \end{bmatrix}</math> |
| − | <math>\Rightarrow | + | <math>\Rightarrow \qquad Not \quad controllable. \qquad Subspace \begin{bmatrix} |
| − | Not controllable | + | |
| − | + | ||
| − | Subspace | + | |
1 \\ | 1 \\ | ||
-3 | -3 | ||
| − | \end{ | + | \end{bmatrix}</math> |
| + | |||
| + | <math>\mathbf{b)} \qquad 0=\begin{bmatrix} | ||
| + | C \\ | ||
| + | CA | ||
| + | \end{bmatrix}=\begin{bmatrix} | ||
| + | 3 & 1 \\ | ||
| + | 6 & 2 | ||
| + | \end{bmatrix}</math> | ||
| + | |||
| + | Not observable. | ||
| + | |||
| + | <math>3x_1+r=0 \qquad x_1=-\frac{1}{3}r \qquad span \begin{bmatrix} | ||
| + | 1 \\ | ||
| + | -3 | ||
| + | \end{bmatrix} | ||
Revision as of 04:29, 16 May 2017
AC-2 2011
P1.
$ \mathbf{a)} \qquad C=\begin{bmatrix} B & AB\end{bmatrix}=\begin{bmatrix} 1 & -1 \\ -3 & 3 \end{bmatrix} $
$ \Rightarrow \qquad Not \quad controllable. \qquad Subspace \begin{bmatrix} 1 \\ -3 \end{bmatrix} $
$ \mathbf{b)} \qquad 0=\begin{bmatrix} C \\ CA \end{bmatrix}=\begin{bmatrix} 3 & 1 \\ 6 & 2 \end{bmatrix} $
Not observable.
$ 3x_1+r=0 \qquad x_1=-\frac{1}{3}r \qquad span \begin{bmatrix} 1 \\ -3 \end{bmatrix} $
