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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
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A transfer function of the system does not have pole-zero cancellation...
Answer: b
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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Most Upvoted Answer
A transfer function of the system does not have pole-zero cancellation...
Explanation:

A transfer function of a system is a mathematical representation that relates the output of a system to its input in the frequency domain. Pole-zero cancellation occurs when a pole of the transfer function cancels out a zero of the transfer function. This results in a simplification of the transfer function and can affect the behavior of the system.

If a transfer function of a system does not have pole-zero cancellation, then the following statement is true:

System is completely controllable and observable

This is because:

- If there is no pole-zero cancellation, then the poles and zeros of the transfer function must be distinct. This means that the system is not marginally stable or unstable.
- A system with distinct poles and zeros is always completely controllable and observable. This means that it is possible to control the system from any initial state to any desired state, and it is possible to observe the system's internal state from its inputs and outputs.

Therefore, option B is the correct answer.
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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 observableb)System is completely controllable and observablec)System is observable but uncontrollabled)System is controllable and unobservableCorrect answer is option 'B'. Can you explain this answer?
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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 observableb)System is completely controllable and observablec)System is observable but uncontrollabled)System is controllable and unobservableCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about 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 observableb)System is completely controllable and observablec)System is observable but uncontrollabled)System is controllable and unobservableCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 observableb)System is completely controllable and observablec)System is observable but uncontrollabled)System is controllable and unobservableCorrect answer is option 'B'. Can you explain this answer?.
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