State Transition Matrix MCQ

1. The state transition matrix for the system \dot x = Ax with initial state x(o) is

  1. laplace inverse of [(sI – A)-1x(0)]
  2. laplace inverse of [(sI – A)-1]
  3. eAt x(0)
  4. (sI – A)-1
Answer. b

2. The following relation involving state transition matrix φ(t) does not hold true

  1. φ(t) = I
  2. φ(t) = φ[(t)]-1
  3. φ(t1 – t2) = φ(t1 – t0)φ(t2 – t0)
  4. φ(t1 + t2) = φ(t1)φ(t2)
Answer. a, b and c

3. What is represented by state transition matrix of a system?

  1. Forced response
  2. Step response
  3. Impulse response
  4. Free response
Answer. d
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