Controllability and Observability MCQ

1. Consider a second order system whose state space representation is of the form

$\dot x = Ax + Bu$. If x1(t) = x2(t), then system is

  1. unstable
  2. observable
  3. uncontrollable
  4. controllable
Answer. c

2. For a feedback control system all the roots of the characteristic equation can be placed at the desired location in the s-plane if and only if the system is

  1. observable
  2. controllable

Which of the above statements are correct?

  1. i only
  2. ii only
  3. both i and ii
  4. neither i nor ii
Answer. b

3. A transfer function of a control system does not have pole-zero cancellation. Which one of the following statement is true?

  1. system is controllable but unobservable
  2. system is observable but uncontrollable
  3. system is completely controllable and observable
  4. system is neither controllable nor observable
Answer. c

4. For the system $\dot x = \begin{bmatrix} 2 & 3\\ 0 & 5 \end{bmatrix}x + \begin{bmatrix} 1\\ 0 \end{bmatrix}u$, which of the following statement is true?

  1. The system is uncontrollable and stable.
  2. The system is controllable and stable.
  3. The system is uncontrollable and unstable.
  4. The system is controllable but unstable.
Answer. c