Discussion
A transfer function of control system does not have pole-zero cancellation. Which one of the following statements is correct ?
Answer: B
The system is completely controllable and observable.
A transfer function describes only the part of a system that is both controllable and observable. If a state were uncontrollable or unobservable, the corresponding mode would cancel out of the transfer function as a common pole and zero. So when there is no pole-zero cancellation, the order of the transfer function equals the number of states, and the system is completely controllable and completely observable.
The other options each describe a system with a hidden mode, which would show up as a pole-zero cancellation in its transfer function.
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