Control Systems - State Space Analysis

A system is characterized by the following state equation and output equation (U: input, X: state vector, y: output) $\dot{x} = \begin{bmatrix} a & b \\ -a & 0 \end{bmatrix}x + \begin{bmatrix} 1 \\ 0 \end{bmatrix}u$ $y =...

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 given below $A = \begin{bmatrix} 0 & 1 \\ -...

Consider a system governed by the following equations $\frac{dx_1(t)}{dt} = x_2(t) - x_1(t)$ $\frac{dx_2(t)}{dt} = x_1(t) - x_2(t)$ The initial conditions are such that $x_1(0) < x_2(0) < \infty$. Let $x_{1f} = \lim_{t\t...

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 \\ 2 & 0 \end{bmatrix} \begin{bmatrix} x_1...