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Given the homogeneous state-space equation
Ẋ = 
-3 1 
X 0 -2
The steady state value of
X(t), the initial state value of X(0) = [10 – 10]T , is
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Xss = 0 0 -
Xss = -3 -2 -
Xss = 10 10 -
Xss = ∞ ∞
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Correct Option: A
| Ẋ = | | | X = AX | ||||
Its solution is,
| X(t) = | | £ – 1 [sI – A] – 1 | | X(0) |
| = £ – 1 | | s + 3 | | – 1 | | | ||||
| 0 | s + 2 | -10 |
| = | | e–3t | | | | |||||
| 0 | -10 |
x1̇ = x1 – x2
x2̇ = x2 + u
y = x1 + x2
∴ ẏ = x1̇ + x2 = x1 +u
ẏ |t = 0 = 0 = 1 + 0 = 1
