# State Variable Analysis · Control Systems · GATE EE

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## Marks 1

GATE EE 2014 Set 2
The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr... GATE EE 2006 For a system with the transfer function$$H\left( s \right) = {{3\left( {s - 2} \right)} \over {{s^3} + 4{s^2} - 2s + 1}},\,\,$$the matrix$$A$$in t... GATE EE 2003 A second order system starts with an initial condition of$$\left( {\matrix{ 2 \cr 3 \cr } } \right)$$without any external input. The st... GATE EE 2002 The state transition matrix for the system$$\mathop X\limits^ \bullet = AX\,\,$$with initial state$$X(0)$$is GATE EE 2001 Given the homogeneous state-space equation$$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \ri...
GATE EE 1995
A system is described by the state equation $$\mathop X\limits^ \bullet = AX + BU$$ , The output is given by $$Y=CX$$ Where $$A = \left( {\matrix{ ... GATE EE 1994 The matrix of any state space equations for the transfer function$$C(s)/R(s)$$of the system, shown below in. Figure is ... GATE EE 1993 Consider a second order system whose state space representation is of the form$$\mathop X\limits^ \bullet = AX + BU.$$If$$\,{x_1}\,\,\left( t \ri...
GATE EE 1993
The transfer function for the state variable representation $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = CX + DU,$$ is given by

## Marks 2

GATE EE 2023
Consider the state-space description of an LTI system with matrices $$A = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 2} \cr } } \right],B = \... GATE EE 2017 Set 1 The transfer function of the system$$Y\left( s \right)/U\left( s \right)$$, whose state-space equations are given below is:$$\eqalign{ & \lef...
GATE EE 2017 Set 2
Consider the system described by the following state space representation \eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet \... GATE EE 2016 Set 1 Consider the following state - space representation of a linear time-invariant system.\mathop x\limits^ \bullet \left( t \right) = \left[ {\matrix...
GATE EE 2015 Set 1
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...
GATE EE 2015 Set 2
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 ... GATE EE 2014 Set 3 Consider the system described by the following state space equations\eqalign{ & \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \r... GATE EE 2014 Set 2 The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{ ... GATE EE 2013 The state variable formulation of a system is given as$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \b... GATE EE 2013 The state variable formulation of a system is given as $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \b... GATE EE 2012 The state variable description of an$$LTI$$system is given by$$\left( {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\...
GATE EE 2010
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