1
GATE EE 2017 Set 1
+2
-0.6
The transfer function of the system $$Y\left( s \right)/U\left( s \right)$$ , whose state-space equations are given below is:
\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet \left( t \right)} \cr {\mathop {{x_2}}\limits^ \bullet \left( t \right)} \cr } } \right] = \left[ {\matrix{ 1 & 2 \cr 2 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] + \left[ {\matrix{ 1 \cr 2 \cr } } \right]u\left( t \right) \cr & y\left( t \right) = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}\left( t \right)} \cr {{x_2}\left( t \right)} \cr } } \right] \cr}
A
$${{\left( {s + 2} \right)} \over {\left( {{s^2} - 2s - 2} \right)}}$$
B
$${{\left( {s + 2} \right)} \over {\left( {{s^2} + s - 4} \right)}}$$
C
$${{\left( {s - 4} \right)} \over {\left( {{s^2} + s - 4} \right)}}$$
D
$${{\left( {s + 4} \right)} \over {\left( {{s^2} - s - 4} \right)}}$$
2
GATE EE 2016 Set 1
Numerical
+2
-0
Consider the following state - space representation of a linear time-invariant system.
$$\mathop x\limits^ \bullet \left( t \right) = \left[ {\matrix{ 1 & 0 \cr 0 & 2 \cr } } \right]\,\,x\left( t \right),\,\,y\left( t \right) = {c^T}x\left( t \right),\,c = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$ and
$$x\left( 0 \right) = \left[ {\matrix{ 1 \cr 1 \cr } } \right]$$

The value of $$y(t)$$ for $$t\,\,\, = \,\,{\log _e}2$$ ___________.

3
GATE EE 2015 Set 2
+2
-0.6
For the system governed by the set of equations: \eqalign{ & d{x_1}/dt = 2{x_1} + {x_2} + u \cr & d{x_2}/dt = - 2{x_1} + u \cr & \,\,\,\,\,\,y = 3{x_1} \cr}\$
the transfer function $$Y(s)/U(s)$$ is given by
A
$$3\left( {s + 1} \right)/\left( {{s^2} - 2s + 2} \right)$$
B
$$3\left( {2s + 1} \right)/\left( {{s^2} - 2s + 1} \right)$$
C
$$\left( {s + 1} \right)/\left( {{s^2} - 2s + 1} \right)$$
D
$$3\left( {2s + 1} \right)/\left( {{s^2} - 2s + 2} \right)$$
4
GATE EE 2015 Set 1
+2
-0.6
In the signal flow diagram given in the figure, $${u_1}$$ and $${u_2}$$ are possible inputs whereas $${y_1}$$ and $${y_2}$$ are possible outputs. When would the $$SISO$$ system derived from this diagram be controllable and observable?
A
When $${u_1}$$ is the only input and $${y_1}$$ is the only output
B
When $${u_2}$$ is the only input and $${y_1}$$ is the only output
C
When $${u_1}$$ is the only input and $${y_2}$$ is the only output
D
When $${u_2}$$ is the only input and $${y_2}$$ is the only output
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