## Marks 1

The state transition matrix for the system $$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr
{\mathop {{x_2}}\limits^ \bullet } \cr...

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...

A second order system starts with an initial condition of $$\left( {\matrix{
2 \cr
3 \cr
} } \right)$$ without any external input. The st...

The state transition matrix for the system $$\mathop X\limits^ \bullet = AX\,\,$$ with initial state $$X(0)$$ is

Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{
{ - 3} & 1 \cr
0 & { - 2} \cr
} } \ri...

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{
...

The matrix of any state space equations for the transfer function $$C(s)/R(s)$$ of the system, shown below in. Figure is
...

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...

The transfer function for the state variable representation $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = CX + DU,$$ is given by

## Marks 2

Consider the system described by the following state space representation
$$\eqalign{
& \left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet \...

The transfer function of the system $$Y\left( s \right)/U\left( s \right)$$ , whose state-space equations are given below is:
$$\eqalign{
& \lef...

Consider the following state - space representation of a linear time-invariant system.
$$\mathop x\limits^ \bullet \left( t \right) = \left[ {\matrix...

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
...

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...

Consider the system described by the following state space equations
$$$\eqalign{
& \left[ {\matrix{
{{x_1}} \cr
{{x_2}} \cr
} } \r...

The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{
...

The state variable formulation of a system is given as
$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr
{\mathop {{x_2}}\limits^ \b...

The state variable formulation of a system is given as
$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr
{\mathop {{x_2}}\limits^ \b...

The state variable description of an $$LTI$$ system is given by
$$$\left( {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr
{\mathop {{x_2}}\...

The system $$\mathop X\limits^ \bullet = AX + BU$$ with $$A = \left[ {\matrix{
{ - 1} & 2 \cr
0 & 2 \cr
} } \right],$$ $$B = \l...

A system is described by the following state and output equations
$$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\left( t \right) + {x_2}\left( t...

A system is described by the following state and output equations
$$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\left( t \right) + {x_2}\left( t...

The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is state vector, $$U$$ is input...

The state space equation of a system is described by $$\mathop X\limits^ \bullet = AX + BU,\,\,Y = Cx$$ where $$X$$ is state vector, $$U$$ is input...

A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{
0 & 1 \cr
0 & { - 3} \cr
} } \right)X\le...

A state variable system
$$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{
0 & 1 \cr
0 & { - 3} \cr
} } \right)X\le...

The state variable description of a linear autonomous system is, $$\mathop X\limits^ \bullet = AX,\,\,$$ where $$X$$ is the two dimensional state v...

The following equation defines a separately exited $$dc$$ motor in the form of a differential equation $${{{d^2}\omega } \over {d{t^2}}} + {{B\,d\omeg...

For the system $$X = \left[ {\matrix{
2 & 3 \cr
0 & 5 \cr
} } \right]X + \left[ {\matrix{
1 \cr
0 \cr
} } \right]u,$$ ...

For the system
$$\mathop X\limits^ \bullet = \left[ {\matrix{
2 & 0 \cr
0 & 4 \cr
} } \right]X + \left[ {\matrix{
1 \cr
...

## Marks 5

Obtain a state variable representation of the system governed by the differential equation: $${{{d^2}y} \over {d{t^2}}} + {{dy} \over {dt}} - 2y = u\l...

Consider the state equation $$\mathop X\limits^ \bullet \left( t \right) = Ax\left( t \right)$$
Given : $${e^{AT}} = \left[ {\matrix{
{{e^{ - t}}...

The state-space representation of a system is given by $$\left[ {\matrix{
{\mathop {{X_1}}\limits^ \bullet } \cr
{\mathop {{X_2}}\limits^ \bu...

Determine the transfer function of the system having the following state variable representation:
$$\eqalign{
& X = \left[ {\matrix{
0 & ...