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A transfer function of the system does not have pole-zero cancellation? Which of the following statements is true?

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A transfer function of the system does not have pole-zero cancellation? Which of the following statements is true?

(a) System is neither controllable nor observable

(b) System is completely controllable and observable

(c) System is observable but uncontrollable

(d) System is controllable and unobservable

I got this question in an interview.

This question is from Controlability and Observability in chapter State Variable Analysis and Design of Control Systems

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Right choice is (b) System is completely controllable and observable

Easy explanation: If the transfer function of the system does not have pole-zero cancellation then it is completely controllable and observable.

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