The state diagram of a system is shown below is described by the state -variable equations: ˙x=AX+Bu;y=CX+Du
The state -variable equations of the system in the figure above are
A
˙X=[−101−1]X+[−11]uy=[1−1]X+u
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B
˙X=[−10−1−1]X+[−11]uy=[−1−1]X+u
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C
˙X=[−101−1]X+[−11]uy=[−1−1]X−u
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D
X=[−1−10−1]X+[−11]uy=[1−1]X−u
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Solution
The correct option is A˙X=[−101−1]X+[−11]uy=[1−1]X+u
So, ˙x1=−x1−u ˙x2=−(x2+x1)=−(x2−x1−u) ˙x2=x1−x2+u y=˙x2 y=x1−x2+u [˙x1˙x2]=[−101−1][x1x2]+[−11]u ˙x=[−101−1]X+[−11]u