GATE EE Question of the Day 10-07-2020

Question of the Day

GATE 2009 EE Question No. 56

A system is described by the following state and output equations

$\frac{d x_{1} (t)}{d t} = - 3 x_{1} (t) + x_{2} (t) + 2 u (t)$

$\frac{d x_{2} (t)}{d t} = - 2 x_{2} (t) + u (t)$

$y (t) = x_{1} (t)$

where u(t) is the input and y(t) is the output

The state transition matrix of the above system is

(A) $[\begin{matrix} e^{- 3 t} & 0 \\ e^{- 2 t} + e^{- 3 t} & e^{- 2 t} \end{matrix}]$
(B) $[\begin{matrix} e^{- 3 t} & e^{- 2 t} - e^{- 3 t} \\ 0 & e^{- 2 t} \end{matrix}]$
(C) $[\begin{matrix} e^{- 3 t} & e^{- 2 t} + e^{- 3 t} \\ 0 & e^{- 2 t} \end{matrix}]$
(D) $[\begin{matrix} e^{3 t} & e^{- 2 t} - e^{- 3 t} \\ 0 & e^{- 2 t} \end{matrix}]$

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Question of the Day 10-07-2020