The state variable formulation of a system is given as
$\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ and $y=\begin{bmatrix} 1 & 0 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}$
The response $y (t)$ to a unit step input is
- $\dfrac{1}{2}-\dfrac{1}{2}e^{-2t} \\$
- $1-\dfrac{1}{2}e^{-2t}-\dfrac{1}{2}e^{-t} \\$
- $e^{-2t}-e^{-t} \\$
- $1-e^{-t}$