Control Systems - State Space Analysis

The state and output equations for a control system are: $\dot{x} = \begin{bmatrix} -4 & -1.5 \\ 4 & 0 \end{bmatrix}x + \begin{bmatrix} 2 \\ 0 \end{bmatrix}u$ $y = \begin{bmatrix} 1.5 & 0.625 \end{bmatrix} x$ Which of th...

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 $\frac{d}{dt} \begin{bmatrix} x_1(t)...

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 space representations given b...

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 $v_1$ and $v_2$ are the corresponding eigenv...

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 system, and y(t) is its output. Let $B =...