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Question

The state model of a system is given as,

[˙x1˙x2]=[1011][x2x1]

xT(0)=[1 0]
The solution of homogenous equation is given by,

A
x(t)=[et1]
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B
x(t)=[ettet]
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C
x(t)=[0et]
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D
x(t)=[etet]
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Solution

The correct option is B x(t)=[ettet]
x(t)=ϕ(t) x(0)
Where, ϕ(t)= state transition matrix
Given, A=[1011]

[sIA]=[s00s][1011]=[s101s1]

[sIA]1=1(s1)(s1)[s101s1]

⎢ ⎢ ⎢1s101(s1)21(s1)⎥ ⎥ ⎥

L1[sIA]1=ϕ(t)=[et0tetet]

x(t)=[et0tetet][10]

x(t)=[ettet]

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