-
Which one of the following systems is completely state controllable?
-
-
x1̇ 
= -1 0 x1 + 2 u x2̇ 0 -2 x2 1 -
x1̇ = -1 0 x1 + 2 u x2̇ 0 -2 x2 0 -
x1̇ = 1 1 x1 + 1 u x2̇ 0 -1 x2 0 -
x1̇ = 0 0 x1 + 2 u x2̇ 2 -2 x2 2
-
Correct Option: A
| [A] = | | -1 | | , [B] = | | 2 | | ||||
| 0 | -2 | 1 |
Now, composite matrix,
| Qc = [B : AB] = | | | |||||
| then , det Qc = | | | ≠ 0 , | ||||
and rank = r = n = 2 and system is completely controllable.
