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Control system miscellaneous

  1. The value of A matrix in ẋ = Ax for the system describe by the different equation
    ẏ̇ + 2 ẏ + 3y = 0, is
    1. 1
      0
      -2-1
    2. 1
      0
      -1-2
    3. 0
      1
      -2-1
    4. 0
      1
      -3-2
Correct Option: D

Let x1 = y
and x2 = x1̇ = ẏ
∴ x2̇ = x1̇̇ = ẏ̇
ẏ̇ + 2 ẏ + 3y = 0
x2̇ + 2x2 + 3x1 = 0
x2̇ = – 3x1 – 2x2
x1̇ = x2

x1̇ = 0
1
x1
x2-3-2x2

∴ A =
0
1
-3
-2



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