State Space

A system is characterized by the following state equation and output equation (U: input, X: state vector, y: output) $\dot{x} = \begin{bmatrix} a & b \\ -a & 0 \end{bmatrix}x + \be...

A system is represented in state-space form as follows: ($u$: input, $\mathbf{x}$: state vector, $y$: output) $\dot{\mathbf{x}}} = \begin{bmatrix} 1 & 2 \\ -3 & 0 \end{bmatrix} \ma...

Consider the state-space model $\dot{x}(t) = Ax(t) + Br(t)$, $y(t) = Cx(t)$ where $x(t)$, $r(t)$, $y(t)$ are the state, input and output, respectively. The matrices A, B, C are giv...

Consider the state-space model $$ \begin{aligned} \dot{x}(t) & =A x(t)+B u(t) \\ y(t) & =C x(t) \end{aligned} $$ where $x(t), r(t), y(t)$ are the state, input and output, respectiv...

Consider the state-space description of an LTI system with matrices A = $\begin{bmatrix} 0 & 1 \ -1 & -2 \end{bmatrix}$, B = $\begin{bmatrix} 0 \ 1 \end{bmatrix}$, C = $\begin{bmat...

Consider the state-space description of an LTI system with matrices $$A = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 2} \cr } } \right],B = \left[ {\matrix{ 0 \cr 1 \cr } } \right],C...

$$ \text { The state space representation of a first-order system is given as } $$ $$ \begin{aligned} & \dot{x}=-x+u \\ & y=x \end{aligned} $$ Where, $x$ is the state variable, $u$...

The transfer function of the system Y(s)/U(s) whose state-space equations are given below is: $\begin{bmatrix} \dot{x_1}(t) \\ \dot{x_2}(t) \end{bmatrix} = \begin{bmatrix} 1 & 2 \\...

Consider the system described by the following state space representation $\begin{bmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 0 & -2 \end{bmatrix...

Consider the system described by the following state space representation $$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet \left( t \right)} \cr {\mathop {{x_2}}\lim...

The transfer function of the system $$Y\left( s \right)/U\left( s \right)$$ , whose state-space equations are given below is: $$\eqalign{ & \left[ {\matrix{ {\mathop {{x_1}}\limits...

For the system governed by the set of equations: $$$\eqalign{ & d{x_1}/dt = 2{x_1} + {x_2} + u \cr & d{x_2}/dt = - 2{x_1} + u \cr & \,\,\,\,\,\,y = 3{x_1} \cr} $$$ the transfer fun...

The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables $$𝑥$$ and...

A discrete system is represented by the difference equation $$$\begin{bmatrix}X_1\left(k+1\right)\\X_2\left(k+2\right)\end{bmatrix}=\begin{bmatrix}a&a-1\\a+1&a\end{bmatrix}\begin{b...

Consider the system described by the following state space equations $$$\eqalign{ & \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 1...

The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr...

The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{ { - 1} & 1 \cr 0 & { - 3} \cr }...

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

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

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

A system is described by the following state and output equations $$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\left( t \right) + {x_2}\left( t \right) + 2u\left( t \right)$$...

A system is described by the following state and output equations $$${{d{x_1}\left( t \right)} \over {dt}} = - 3{x_1}\left( t \right) + {x_2}\left( t \right) + 2u\left( t \right)$$...

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, $$Y$$ is output and $$$A = \lef...

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 the state space form $$\mathop...

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

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

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

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\omega } \over {j\,\,dt}} + {{{K^2}...

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

For the system $$X = \left[ {\matrix{ 2 & 3 \cr 0 & 5 \cr } } \right]X + \left[ {\matrix{ 1 \cr 0 \cr } } \right]u,$$ Which of the following statement is true?

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

Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \right]x$$ the steady state value of $$\,\,{x_{ss}}\,\,...

Determine the transfer function of the system having the following state variable representation: $$\eqalign{ & X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr { - 40} & { - 44} &...

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{ { - 4} & { - 1} \cr 3 & { - 1} \c...

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

Consider a second order system whose state space representation is of the form $$\mathop X\limits^ \bullet = AX + BU.$$ If $$\,{x_1}\,\,\left( t \right)\, = {x_2}\,\left( t \right)...