1
GATE ECE 2024
MCQ (More than One Correct Answer)
+2
-1.33
Consider a system $S$ represented in state space as
$$\frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix}x + \begin{bmatrix} 1 \\ 0 \end{bmatrix}r , \quad y = \begin{bmatrix} 2 & -5 \end{bmatrix}x.$$
Which of the state space representations given below has/have the same transfer function as that of $S$?
2
GATE ECE 2018
MCQ (Single Correct Answer)
+2
-0.67
The state equation and the output equation of a control system are given below:
$$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matrix{ 2 \cr 0 \cr } } \right]u,$$
$$y = \left[ {\matrix{ {1.5} & {0.625} \cr } } \right]x.$$
The transfer function representation of the system is
$$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matrix{ 2 \cr 0 \cr } } \right]u,$$
$$y = \left[ {\matrix{ {1.5} & {0.625} \cr } } \right]x.$$
The transfer function representation of the system is
3
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+2
-0.6
A second order LTI system is described by the following state equation.
$$$\eqalign{
& {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \right) = 0 \cr
& {d \over {dt}}{x_2}\left( t \right) + 2{x_1}\left( t \right) + 3{x_2}\left( t \right) = r\left( t \right) \cr} $$$
When x1(t) and x2(t) are the two state variables and r(t) denotes the input. The output c(t)=X1(t). The systyem is
4
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+2
-0.6
A second-order linear time-invariant system is described by the following state equations
$$$\eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_1}\left( t \right) = 3u\left( t \right) \cr
& {d \over {dt}}{x_2}\left( t \right) + {x_2}\left( t \right) = u\left( t \right) \cr} $$$
Where x1(t), then the system is
Questions Asked from State Space Analysis (Marks 2)
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GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics