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The system Ẋ = 
2 3 
X + 1 u is 0 5 0
-
- controllable but unstable
- uncontrollable and unstable
- controllable and stable
- uncontrollable and stable
Correct Option: B
| Ẋ = | | 2 | | X + | | | u | ||||
| 0 | 0 |
| B = | | 1 | | , A = | | 2 | | |||
| 0 | 0 | 5 |
| AB = | | 2 | | | | = | | | |||||
| 0 | 0 | 0 |
| ⇒ [B : AB] = | | | |||||
This is not a 2 × 2 matrix, hence system is uncontrollable
| Now [sI - A] = | | s | | - | | 2 | 3 | | ||||||
| 0 | s | 0 | 5 |
| = | | | |||||
= (s – 2) (s – 5)
Two roots on positive half of the y-axis, hence the system is unstable .
