## 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 More Consider the system described by the following state space representation \eqalign{ & \left[ {\matrix{ {\mathop ... GATE EE 2017 Set 2 The transfer function of the systemY\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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