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A linear time-invariant system describd by the state variable model
X1̇ 
= -1 0 X1 + 0 u = [ 1 2 ] X1 X2̇ 0 -2 X2 1 X2
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- is completely controllable
- is not completely controllable
- is completely observable
- is not completely observable
- Both B and C options
Correct Option: E
The linear time-invariant system:
| X1̇ | | = | | -1 | | | X1 | | + | | 1 | | u | = [ 1 2 ] | | X1 | | |||
| X2̇ | 1 | -2 | X2 | 0 | X2 |
| A = | | -1 | | , B = | | | , C = [1 2] | ||||
| 1 | 1 |
| [B AB] = | | | = |B AB| = 0 | ||||
Hence not completely controllable
| [CT ATCT] = | | | |||||
[CT ATCT] ≠ 0
Hence observable.
