Consider the following state-space representation of a linear time-invariant system. ˙{x}(t)=\left[\begin{array}{cc}1 & 0 \ 0 & 2]\end{array} x(t), y(t)=c^T x(t), c=\left[\begin{array}{c}1 \ 1]\end{array} and x(0)=\left[\begin{array}{c}1 \ 1]\end{array} The value of y (t) for t = \log _{e}2 is __________.

GATE Electrical Engineering (EE) 2016 Shift 1 Solved Paper

Question : 41 of 65

Marks: +1, -0

Consider the following state-space representation of a linear time-invariant system.

˙{x}(t)={[\table 1 , 0 ; 0 , 2]} x(t), y(t)=c^T x(t), c={[\table 1 ; 1]}

and

x(0)={[\table 1 ; 1]}

The value of

y (t)

for

t = \log _{e}2

is __________.

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