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1

### 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 $$A = \left( {\matrix{ { - 4} & { - 1} \cr 3 & { - 1} \cr } } \right)\,\,B = \left( {\matrix{ 1 \cr 1 \cr } } \right)\,\,C = \left[ {10} \right]$$

Transfer function $$G(s)$$ of the system is

A
$${s \over {{s^2} + 5s + 7}}$$
B
$${1 \over {{s^2} + 5s + 7}}$$
C
$${s \over {{s^2} + 3s + 2}}$$
D
$${1 \over {{s^2} + 3s + 2}}$$
2

### 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 A
$$\left( {\matrix{ { - 1} & 0 \cr 0 & 1 \cr } } \right)$$
B
$$\left( {\matrix{ 1 & 0 \cr 0 & { - 1} \cr } } \right)$$
C
$$\left[ { - 1} \right]$$
D
$$\left[ { 3} \right]$$
3

### GATE EE 1993

The transfer function for the state variable representation $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = CX + DU,$$ is given by
A
$$D + C{\left( {s{\rm I} - A} \right)^{ - 1}}\,\,B$$
B
$$B{\left( {s{\rm I} - A} \right)^{ - 1}}\,C + D$$
C
$$D{\left( {s{\rm I} - A} \right)^{ - 1}}\,B + C$$
D
$$C{\left( {sl - A} \right)^{ - 1}}\,D + B$$
4

### GATE EE 1993

Consider a second order system whose state space representation is of the form $$\mathop X\limits^ \bullet = AX + BU.$$ If $$\,{x_1}\,\,\left( t \right)\, = {x_2}\,\left( t \right),$$ then system is
A
controllable
B
uncontrollable
C
observable
D
unstable
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#### Questions Asked from State Variable Analysis

On those following papers in Marks 1
Number in Brackets after Paper Indicates No. of Questions
GATE EE 2014 Set 2 (1)
GATE EE 2006 (1)
GATE EE 2003 (1)
GATE EE 2002 (1)
GATE EE 2001 (1)
GATE EE 1995 (1)
GATE EE 1994 (1)
GATE EE 1993 (2)

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Class 12