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State representation of a second order system is
x1̇ = -x1 + u
x2̇ = x1 - 2x2 + u
Consider the following statements regarding the above system :
1. The system is completely state controllable
2. If x1 is the output, then the system is completely output controllable
3. If x2 is the output, then the system is completely output controllable. Of these statements
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- 1, 2 and 3 are correct
- 1 and 2 are correct
- 2 and 3 are correct
- 1 and 3 are correct
Correct Option: C
x1̇ = -x1 + u ; x2̇ = x1 - 2x2 + u
| ∴ A = |  | -1 |  | ; B = | | 1 | | ||||
| 1 | -2 | 1 |
For the system to be state controllable,
| B : AB = | | 1 | | |||
| 1 | -1 |
Therefore, the system is not state controllable. Hence, all the responses containing statement 1 is incorrect.
