## Marks 1

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Consider the state space realization $$\left[ {\matrix{ {\mathop x\limits^ \bullet } & {\left( t \right)} \cr ... GATE ECE 2017 Set 2 Consider the system$${{dx} \over {dt}} = Ax + Bu$$with$${\rm A} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr }...
GATE ECE 2009
A linear system is equivalently represented by two sets of state equations. $$\mathop x\limits^ \bullet = \,\,{\rm A}X... GATE ECE 2005 The transfer function Y(s)/U(s) of a system described by the state equations$$\mathop x\limits^ \bullet $$(t) = -2x(t... GATE ECE 2002 The system mode described by the state equations$$X = \left( {\matrix{ 0 & 1 \cr 2 & { - 3} \cr } } \right... GATE ECE 1999 ## Marks 2 More A second order LTI system is described by the following state equation. \eqalign{ & {d \over {dt}}{x_1}\left( t \ri... GATE ECE 2017 Set 2 A second-order linear time-invariant system is described by the following state equations\eqalign{& {d \over {dt}}{x...
GATE ECE 2016 Set 3
A network is described by the state model as \eqalign{ & {\mathop x\limits^ \bullet _1} = 2{x_1} - {x_2} + 3u, \c... GATE ECE 2015 Set 3 The state variable representation of a system is given as\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix... GATE ECE 2015 Set 2 The state transition matrix $$\phi \left( t \right)$$ of a system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bu... GATE ECE 2014 Set 4 The state equation of a second-order linear system is given by$$\mathop x\limits^ \bullet \left( t \right) = Ax\left( ... GATE ECE 2014 Set 3 An unforced linear time invariant (LTI) system is represented by $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet... GATE ECE 2014 Set 2 Consider the state space system expressed by the signal flow diagram shown in the figure. The corresponding system is... GATE ECE 2014 Set 2 Consider the state space model of a system, as given below The system is... GATE ECE 2014 Set 1 The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equat... GATE ECE 2013 The state diagram of a system is shown below. A system is shown below. A system is described by the state variable equat... GATE ECE 2013 The state variable description of an LTI system is given by where y is the output and u is input. The system is contro... GATE ECE 2012 The block diagram of a system with one input u and two outputs y1 and y2 is given below A state space model of the abo... GATE ECE 2011 The signal flow graph of a system is shown below. The state variable representation of the system can be ... GATE ECE 2010 The signal flow graph of a system is shown below. The transfer function of the system is... GATE ECE 2010 A signal flow graph of a system is given below. The set of equations that correspond to this signal flow graph is... GATE ECE 2008 Consider a linear system whose state space Representation is$$\mathop x\limits^ \bullet \left( t \right) = AX\left( t ... GATE ECE 2007 Consider a linear system whose state space Representation is $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t ... GATE ECE 2007 The state space representation of a separately excited DC servo motor dynamics is given as$$\left[ {\matrix{ {{{d\o...
GATE ECE 2007
A linear system is described by the following state equation $$\mathop x\limits^ \bullet \left( t \right) = AX\left( t... GATE ECE 2006 The state variable equations of a system are:$$${\mathop {{x_1} = - 3{x_1} - x}\limits^ \bullet _2} + u${\matho...
GATE ECE 2004
Given A $$= \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the state transition matrix eAt...
GATE ECE 2004
If A = $$\left[ {\matrix{ { - 2} & 2 \cr 1 & { - 3} \cr } } \right],$$ then sin At is
GATE ECE 2004
The zero, input response of a system given by the state space equation $$\left[ {{{\mathop {{x_1}}\limits^ \bullet } \... GATE ECE 2003 For the system described by the state equation$$$\mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 & 0 \c... GATE ECE 1999 A certain linear time invariant system has the state and the output equations given below $$\left[ {\matrix{ {\mat... GATE ECE 1997 A linear time-invariant system is described by the state variable model$$$\left[ {\matrix{ {{{\mathop x\limits^ \bul...
GATE ECE 1992
A linear second order single input continuous-time system is described by the following set of differential equations ...
GATE ECE 1991

## Marks 5

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The block diagram of a linear time invariant system is given in Figure is (a) Write down the state variable equations...
GATE ECE 2002
A certain linear, time-invariant system has the state and output representation shown below: \eqalign{ & \left[ {\m... GATE ECE 2000 For the circuit shown in the figure, choose state variables as{x_{1,}}{x_{2,}}{x_3}$$to be$${i_{L1}}\left( t \rig...
GATE ECE 1997
Obtain a state space representation in diagonal form for the following system \${{{d^3}y} \over {d{t^3}}} + 6{{{d^2}y} ...
GATE ECE 1996

## Marks 10

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A system is characterized by the following state-space equations: a) Find the transfer function of the system b) Comput...
GATE ECE 1990

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