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The linear time invariant system is represented by the state space model as

Consider n=number of state variables, m = number of inputs, p= number of outputs. The state transition matrix Φ( t) Φ( t) is given by:
  • a)
    Φ(t) = [(SI-A)]-1
  • b)
    Φ(t) = L-1 [(SI-A)]-1
  • c)
    Φ(t) = L[(SI-A)]-1
  • d)
    Φ(t) = L-1 [(SI-A)]
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The linear time invariant system is represented by the state space mod...
Concept:
The state transition matrix [ϕ(t)] is given by:
ϕ(t) = eAt = L-1 [(SI-A)]-1
where, A = System matrix
I = Identity matrix
Properties of state transition matrix:
(1) State transition matrix at t = 0 is always equal to the identity matrix. 
ϕ(0) = eA0 = I
(2) The differentiation of the state transition matrix at t = 0 is always equal to its system matrix.
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Most Upvoted Answer
The linear time invariant system is represented by the state space mod...
Concept:
The state transition matrix [ϕ(t)] is given by:
ϕ(t) = eAt = L-1 [(SI-A)]-1
where, A = System matrix
I = Identity matrix
Properties of state transition matrix:
(1) State transition matrix at t = 0 is always equal to the identity matrix. 
ϕ(0) = eA0 = I
(2) The differentiation of the state transition matrix at t = 0 is always equal to its system matrix.
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The linear time invariant system is represented by the state space model asConsider n=number of state variables, m = number of inputs, p= number of outputs. The state transition matrix Φ( t) Φ( t) is given by:a)Φ(t) = [(SI-A)]-1b)Φ(t) = L-1 [(SI-A)]-1c)Φ(t) = L[(SI-A)]-1d)Φ(t) = L-1 [(SI-A)]Correct answer is option 'B'. Can you explain this answer?
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The linear time invariant system is represented by the state space model asConsider n=number of state variables, m = number of inputs, p= number of outputs. The state transition matrix Φ( t) Φ( t) is given by:a)Φ(t) = [(SI-A)]-1b)Φ(t) = L-1 [(SI-A)]-1c)Φ(t) = L[(SI-A)]-1d)Φ(t) = L-1 [(SI-A)]Correct 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 The linear time invariant system is represented by the state space model asConsider n=number of state variables, m = number of inputs, p= number of outputs. The state transition matrix Φ( t) Φ( t) is given by:a)Φ(t) = [(SI-A)]-1b)Φ(t) = L-1 [(SI-A)]-1c)Φ(t) = L[(SI-A)]-1d)Φ(t) = L-1 [(SI-A)]Correct 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 The linear time invariant system is represented by the state space model asConsider n=number of state variables, m = number of inputs, p= number of outputs. The state transition matrix Φ( t) Φ( t) is given by:a)Φ(t) = [(SI-A)]-1b)Φ(t) = L-1 [(SI-A)]-1c)Φ(t) = L[(SI-A)]-1d)Φ(t) = L-1 [(SI-A)]Correct answer is option 'B'. Can you explain this answer?.
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