17. If the real part of a pole is positive, then output response a) grows towards infinity. b) decreases towards zero. c) remains constant d) can be either (a) or (b) or (c) 18. Choose the correct statement: a) Stable systems are always controllable. b) Stable systems are always observable. c) Stable systems are always controllable and observable. d) Stability is not necessary for controllability and observability.

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17. If the real part of a pole is positive, then output response
a) grows towards infinity.
b) decreases towards zero.
c) remains constant
d) can be either (a) or (b) or (c)
18. Choose the carrect statement:
a) Stable systems are always controllable.
b) Stable systems are always observable.
c) Stable systems are always controllable and observable.
d) Stability is not necessary for controllability and observability.
19. Consider the system, X = AX + BU where xis state vector, A is the system matrix, B is the input matrix anduis the input
vector. Assume xas the initial state and tas the initial time. Then the solution of the system depends on
a) U,X,t,A
b) U,X,t,A, B
X,t,A, B
d) x,t
20. Knowledge of complete state trajectory is must for determining system stability:
a) True for linear time invariant system.
b) Not always true for nonlinear system.
c) Both (a) and (b).
d) True for linear and nonlinear systems.
21. Uncontrollable and unobservable states arise due to
a) redundant state variables.
b) physically uncontrollable system.
c) too much symmetry.
d) all of the above.
22. Consider the following assumptions for the pole placement control design:
(1) The system is completely state controllable.
(2) The state variables are measurable and available for feedback.
(3) The system is observable.
(4) Control input is unconstrained.
Choose the correct ones,
a) (1), (2) and (3)
b) (1), (2) and (4)
c) (1), (3) and (4)
d) (2), (3) and (4)
23. Which of the following is true for Separation principle:
a) Controller design and observer design may not be independent of each other..
b) Controller design and observer design always dependent on each other.
c) Controller design and observer design are independent of each other.
d) None of these.
24. For stabilizable system:
a) Uncontrollable states are unstable.
b) Uncontrollable states are stable.
c) Unobservable states are stable.
d) Unobservable states are unstable.
25. Which of the following conditions are required for observer design:
a) Observability condition must be satisfied.
b) Observability condition needs not be satisfied.
c) Controllability condition must be satisfied.
d) None of these.
Transcribed Image Text:17. If the real part of a pole is positive, then output response a) grows towards infinity. b) decreases towards zero. c) remains constant d) can be either (a) or (b) or (c) 18. Choose the carrect statement: a) Stable systems are always controllable. b) Stable systems are always observable. c) Stable systems are always controllable and observable. d) Stability is not necessary for controllability and observability. 19. Consider the system, X = AX + BU where xis state vector, A is the system matrix, B is the input matrix anduis the input vector. Assume xas the initial state and tas the initial time. Then the solution of the system depends on a) U,X,t,A b) U,X,t,A, B X,t,A, B d) x,t 20. Knowledge of complete state trajectory is must for determining system stability: a) True for linear time invariant system. b) Not always true for nonlinear system. c) Both (a) and (b). d) True for linear and nonlinear systems. 21. Uncontrollable and unobservable states arise due to a) redundant state variables. b) physically uncontrollable system. c) too much symmetry. d) all of the above. 22. Consider the following assumptions for the pole placement control design: (1) The system is completely state controllable. (2) The state variables are measurable and available for feedback. (3) The system is observable. (4) Control input is unconstrained. Choose the correct ones, a) (1), (2) and (3) b) (1), (2) and (4) c) (1), (3) and (4) d) (2), (3) and (4) 23. Which of the following is true for Separation principle: a) Controller design and observer design may not be independent of each other.. b) Controller design and observer design always dependent on each other. c) Controller design and observer design are independent of each other. d) None of these. 24. For stabilizable system: a) Uncontrollable states are unstable. b) Uncontrollable states are stable. c) Unobservable states are stable. d) Unobservable states are unstable. 25. Which of the following conditions are required for observer design: a) Observability condition must be satisfied. b) Observability condition needs not be satisfied. c) Controllability condition must be satisfied. d) None of these.
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