GATE 2013 Electrical Engineering PYQ

Question

The state variable formulation of a system is given as
$$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ { - 2} & 0 \cr 0 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u,\,\,{x_1}\left( 0 \right) = 0,$$
$${x_2}\left( 0 \right) = 0$$ and $$y = \left[ {\matrix{ 1 & 0 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$

The response $$y(t)$$ to a unit step input is

Accepted Answer

$${1 \over 2} - {1 \over 2}{e^{ - 2t}}$$

Answer

$$1 - {1 \over 2}{e^{ - 2t}} - {1 \over 2}{e^{ - t}}$$

Answer

$${e^{ - 2t}} - {e^{ - t}}$$

Answer

$$1 - {e^{ - t}}$$