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GATE 2023 Control system Quiz 68
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Question 1
Consider the state-transition matrix of a LTI system is given by 
and having initial state as 
and the input signal as 
. Where 
is the unit-step input signal. Then the zero-input response of the system is given by
and having initial state as and the input signal as . Where is the unit-step input signal. Then the zero-input response of the system is given by Question 2
Let the state transition matrix of a system be given as
Then which of the following is equal to
Then which of the following is equal to
Question 3
A certain linear time invariant system has the state and output equations give below
y = [1 1] 
If X1(0) = 1
X2(0) = –1
U(0) = 0 then 
at t =0 is ___
Question 4
The state transition matrix of a system is given below:
Find the characteristic equation of the system.
Find the characteristic equation of the system.
Question 5
Consider the electrical network shown in the figure below along with its state equation
The state matrix A is equal to
Question 6
A system is described by the following state equations and output equation
Where u (t) is the input and y(t) is the output. The state-transition matrix of the above system is
Where u (t) is the input and y(t) is the output. The state-transition matrix of the above system is
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Jul 20ESE & GATE EC
