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The second order dynamic system
dX = PX + Qu y = RX dt
has the matrices P, Q and R as follows :P = 
-1 1 
, Q = 0 , R = [0 1] 0 -3 1
The system has the following controllability and observability properties :
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- Controllable and observable
- Not controllable but observable
- Controllable but not observable
- Not controllable and not observable
Correct Option: C
For controllability,
MC = [Q PQ]
| MC = | | | |||||
| 1 |
Therefore, the system is Controllable.
Now, for observability.
| M0 = [RT RT pT ] = | | | |||||
| 1 |
Therefore, the system is not observable.
