state space

The state and output equations for a control system are: $\dot{x} = \begin{bmatrix} -4 & -1.5 \\ 4 & 0 \end{bmatrix}x + \begin{bmatrix} 2 \\ 0 \end{bmatrix}u$ $y = \begin{bmatrix}...

Consider a system where $x_1(t)$, $x_2(t)$, and $x_3(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the system are given...

Consider a system where $x_1(t), x_2(t)$, and $x_3(t)$ are three internal state signals and $u(t)$ is the input signal. The differential equations governing the system are given by...

Consider a system $S$ represented in state space as $\frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix}x + \begin{bmatrix} 1 \\ 0 \end{bmatrix}r, y=[2 \ -5]x$. Which of...

The state equation of a second order system is $\dot{x}(t) = Ax(t)$, $x(0)$ is the initial condition. Suppose $\lambda_1$ and $\lambda_2$ are two distinct eigenvalues of A and $v_1...

Let the state-space representation of an LTI system be $\dot{x}(t) = A x(t) + B u(t)$, $y(t) = C x(t) + d u(t)$ where A, B, C are matrices, d is a scalar, u(t) is the input to the...

The state equation and the output equation of a control system are given below: $$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matr...

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

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 \right) = 0 \cr & {d \over {dt}}{x_2}\lef...

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_1}\left( t \right) = 3u\left( t \r...

The state variable representation of a system is given as $$$\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 \cr 0 & { - 1} \cr } } \right]x;x\left( 0 \right) = \lef...

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}}\limits^ \bullet = - 4{x_2} - u, \cr & y = 3{...

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

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

The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left( t \right),x\left( 0 \right) = {x_0}.$$ For $${x_0} = \left[ {...

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

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

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

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

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),A = \left[ {\matrix{ 0 & 1 \cr...

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

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

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

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

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

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

A certain linear, time-invariant system has the state and output representation shown below: $$$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}...

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

For the system described by the state equation $$$\mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr {0.5} & 1 & 2 \cr } } \right]x + \left[ {\matrix{ 0 \cr 0...

A certain linear time invariant system has the state and the output equations given below $$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bulle...

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} \over {dt}} + 6y = 6u\left( t \rig...

A linear time-invariant system is described by the state variable model $$$\left[ {\matrix{ {{{\mathop x\limits^ \bullet }_1}} \cr {{{\mathop x\limits^ \bullet }_2}} \cr } } \right...

A linear second order single input continuous-time system is described by the following set of differential equations $$$\eqalign{ & \mathop {{x_1}}\limits^ \bullet \left( t \right...