GATE EC 2026 Set 1 — Question 41
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Control Systems → State-Space Analysis → Transfer Function from States
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Question
The state and output equations for a control system are:
Which of the following expressions correctly represents the transfer function of the system with zero initial conditions?
Which of the following expressions correctly represents the transfer function of the system with zero initial conditions?
Correct answer
(C) (3s+5)/(s²+4s+6)
Solution
The state-space representation of a system is given by:
From the given equations, we have:
(since there is no direct feedthrough term from to )The transfer function for a system with zero initial conditions is given by:
First, calculate :
Next, calculate the determinant of :
Now, calculate :
Now, calculate :
First, multiply :
Now, multiply by :
Since , the transfer function is .The final answer is
From the given equations, we have:
(since there is no direct feedthrough term from to )The transfer function for a system with zero initial conditions is given by:
First, calculate :
Next, calculate the determinant of :
Now, calculate :
Now, calculate :
First, multiply :
Now, multiply by :
Since , the transfer function is .The final answer is
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