State Space Analysis · Control Systems · GATE ECE

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

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

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

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 ...

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

Consider a system $S$ represented in state space as$$\frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix}x + \begin{bmatrix} 1 \\ 0 \end{bma...

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

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...

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_...

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

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}}...

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

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) = ...

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

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

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

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...

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...

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...

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...

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

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

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

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

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

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

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),...

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

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

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...

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

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

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

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

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

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...

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

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),{...

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...

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