# State Space Analysis · Control Systems · GATE ECE

Start Practice## Marks 1

GATE ECE 2017 Set 2

Consider the state space realization
$$$\left[ {\matrix{
{\mathop x\limits^ \bullet } & {\left( t \right)} \cr
{\mathop x\limits^ \bullet...

GATE ECE 2009

Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\matrix{
1 & 0 \cr
0 & 1 \cr
} } \right]\,\,\,and\,\...

GATE ECE 2005

A linear system is equivalently represented by two sets of state equations. $$\mathop x\limits^ \bullet = \,\,{\rm A}X\,\, + BU$$ and $$\mathop W\li...

GATE ECE 2002

The transfer function Y(s)/U(s) of a system described by the state equations
$$\mathop x\limits^ \bullet $$(t) = -2x(t)+2u(t)
y(t) = 0.5x(t) is
...

GATE ECE 1999

The system mode described by the state equations
$$$X = \left( {\matrix{
0 & 1 \cr
2 & { - 3} \cr
} } \right)x + \left( {\matrix{
...

## Marks 2

GATE ECE 2018

The state equation and the output equation of a control system are given below:
$$\mathop x\limits^. = \left[ {\matrix{
{ - 4} & { - 1.5} \cr...

GATE ECE 2017 Set 2

A second order LTI system is described by the following state equation.
$$$\eqalign{
& {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \righ...

GATE ECE 2016 Set 3

A second-order linear time-invariant system is described by the following state equations
$$$\eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_...

GATE ECE 2015 Set 2

The state variable representation of a system is given as
$$$\eqalign{
& \mathop x\limits^ \bullet = \left[ {\matrix{
0 & 1 \cr
0 ...

GATE ECE 2015 Set 3

A network is described by the state model as
$$$\eqalign{
& {\mathop x\limits^ \bullet _1} = 2{x_1} - {x_2} + 3u, \cr
& \mathop {{x_2}}...

GATE ECE 2014 Set 4

The state transition matrix $$\phi \left( t \right)$$ of a system $$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr
{\mathop {{x_2}...

GATE ECE 2014 Set 3

The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left( t \right),x\left( 0 \right) = ...

GATE ECE 2014 Set 2

An unforced linear time invariant (LTI) system is represented by
$$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr
{\mathop {{x_2}}\...

GATE ECE 2014 Set 2

Consider the state space system expressed by the signal flow diagram shown in the figure.
The corresponding system is...

GATE ECE 2014 Set 1

Consider the state space model of a system, as given below
The system is...

GATE ECE 2013

The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equations
The state transition m...

GATE ECE 2013

The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equations
The state-variable equ...

GATE ECE 2012

The state variable description of an LTI system is given by
where y is the output and u is input. The system is controllable for...

GATE ECE 2011

The block diagram of a system with one input u and two outputs y1 and y2 is given below
A state space model of the above system in terms of the stat...

GATE ECE 2010

The signal flow graph of a system is shown below.
The state variable representation of the system can be
...

GATE ECE 2010

The signal flow graph of a system is shown below.
The transfer function of the system is...

GATE ECE 2008

A signal flow graph of a system is given below.
The set of equations that correspond to this signal flow graph is...

GATE ECE 2007

Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right).$$
If the initial sta...

GATE ECE 2007

Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right).$$
If the initial sta...

GATE ECE 2007

The state space representation of a separately excited DC servo motor dynamics is given as
$$$\left[ {\matrix{
{{{d\omega } \over {dt}}} \cr
{...

GATE ECE 2006

A linear system is described by the following state equation
$$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t \right) + BU\left( t \right),...

GATE ECE 2004

The state variable equations of a system are:
$$${\mathop {{x_1} = - 3{x_1} - x}\limits^ \bullet _2} + u$$$
$$${\mathop x\limits^ \bullet _2} = 2{x...

GATE ECE 2004

If A = $$\left[ {\matrix{
{ - 2} & 2 \cr
1 & { - 3} \cr
} } \right],$$ then sin At is

GATE ECE 2004

Given A $$ = \left[ {\matrix{
1 & 0 \cr
0 & 1 \cr
} } \right],$$ the state transition matrix eAt is given by...

GATE ECE 2003

The zero, input response of a system given by the state space equation
$$$\left[ {{{\mathop {{x_1}}\limits^ \bullet } \over {\mathop {{x_2}}\limits^ ...

GATE ECE 1999

For the system described by the state
equation $$$\mathop x\limits^ \bullet = \left[ {\matrix{
0 & 1 & 0 \cr
0 & 0 & ...

GATE ECE 1997

A certain linear time invariant system has the state and the output equations given below
$$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet } ...

GATE ECE 1992

A linear time-invariant system is described by the state variable model
$$$\left[ {\matrix{
{{{\mathop x\limits^ \bullet }_1}} \cr
{{{\mathop...

GATE ECE 1991

A linear second order single input continuous-time system is described by the
following set of differential equations
$$$\eqalign{
& \mathop {{...

## Marks 5

GATE ECE 2002

The block diagram of a linear time invariant system is given in Figure is
(a) Write down the state variable equations for the system in matrix form...

GATE ECE 2000

A certain linear, time-invariant system has the state and output representation shown below:
$$$\eqalign{
& \left[ {\matrix{
{\mathop {{x_1}}...

GATE ECE 1997

For the circuit shown in the figure, choose state variables as $${x_{1,}}{x_{2,}}{x_3}$$ to be $${i_{L1}}\left( t \right),{v_{c2}}\left( t \right),{...

GATE ECE 1996

Obtain a state space representation in diagonal form for the following system
$$${{{d^3}y} \over {d{t^3}}} + 6{{{d^2}y} \over {d{t^2}}} + 11{{dy} \ove...

## Marks 10

GATE ECE 1990

A system is characterized by the following state-space equations:
a) Find the transfer function of the system
b) Compute the state-transition matrix/...