GATE EE

State Variable Analysis

Control Systems

(Past Years Questions)

Marks 1

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The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {...
GATE EE 2014 Set 2
For a system with the transfer function $$H\left( s \right) = {{3\left( {s - 2} \right)} \over {{s^3} + 4{s^2} - 2s + 1}...
GATE EE 2006
A second order system starts with an initial condition of $$\left( {\matrix{ 2 \cr 3 \cr } } \right)$$ with...
GATE EE 2003
The state transition matrix for the system $$\mathop X\limits^ \bullet = AX\,\,$$ with initial state $$X(0)$$ is
GATE EE 2002
Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & ...
GATE EE 2001
A system is described by the state equation $$\mathop X\limits^ \bullet = AX + BU$$ , The output is given by $$Y=CX$$ ...
GATE EE 1995
The matrix of any state space equations for the transfer function $$C(s)/R(s)$$ of the system, shown below in. Figure is...
GATE EE 1994
Consider a second order system whose state space representation is of the form $$\mathop X\limits^ \bullet = AX + BU.$...
GATE EE 1993
The transfer function for the state variable representation $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = CX + DU,$$ i...
GATE EE 1993

Marks 2

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Consider the system described by the following state space representation $$\eqalign{ & \left[ {\matrix{ {\mathop ...
GATE EE 2017 Set 2
The transfer function of the system $$Y\left( s \right)/U\left( s \right)$$ , whose state-space equations are given belo...
GATE EE 2017 Set 1
Consider the following state - space representation of a linear time-invariant system. $$\mathop x\limits^ \bullet \lef...
GATE EE 2016 Set 1
For the system governed by the set of equations: $$$\eqalign{ & d{x_1}/dt = 2{x_1} + {x_2} + u \cr & d{x_2}/dt = ...
GATE EE 2015 Set 2
In the signal flow diagram given in the figure, $${u_1}$$ and $${u_2}$$ are possible inputs whereas $${y_1}$$ and $${y_2...
GATE EE 2015 Set 1
Consider the system described by the following state space equations $$$\eqalign{ & \left[ {\matrix{ {{x_1}} \cr ...
GATE EE 2014 Set 3
The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as foll...
GATE EE 2014 Set 2
The state variable formulation of a system is given as $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr ...
GATE EE 2013
The state variable formulation of a system is given as $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr ...
GATE EE 2013
The state variable description of an $$LTI$$ system is given by $$$\left( {\matrix{ {\mathop {{x_1}}\limits^ \bullet...
GATE EE 2012
The system $$\mathop X\limits^ \bullet = AX + BU$$ with $$A = \left[ {\matrix{ { - 1} & 2 \cr 0 & 2 \cr }...
GATE EE 2010
A system is described by the following state and output equations $$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\l...
GATE EE 2009
A system is described by the following state and output equations $$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\l...
GATE EE 2009
The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is...
GATE EE 2008
The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is...
GATE EE 2008
A state variable system $$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} ...
GATE EE 2005
A state variable system $$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} ...
GATE EE 2005
The state variable description of a linear autonomous system is, $$\mathop X\limits^ \bullet = AX,\,\,$$ where $$X$$ ...
GATE EE 2004
The following equation defines a separately exited $$dc$$ motor in the form of a differential equation $${{{d^2}\omega }...
GATE EE 2003
For the system $$X = \left[ {\matrix{ 2 & 3 \cr 0 & 5 \cr } } \right]X + \left[ {\matrix{ 1 \cr 0 \...
GATE EE 2002
For the system $$\mathop X\limits^ \bullet = \left[ {\matrix{ 2 & 0 \cr 0 & 4 \cr } } \right]X + \left[ {...
GATE EE 2002

Marks 5

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Obtain a state variable representation of the system governed by the differential equation: $${{{d^2}y} \over {d{t^2}}} ...
GATE EE 2002
Consider the state equation $$\mathop X\limits^ \bullet \left( t \right) = Ax\left( t \right)$$ Given : $${e^{AT}} = \...
GATE EE 2000
The state-space representation of a system is given by $$\left[ {\matrix{ {\mathop {{X_1}}\limits^ \bullet } \cr ...
GATE EE 1998
Determine the transfer function of the system having the following state variable representation: $$\eqalign{ & X = \l...
GATE EE 1997

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