GATE EE 2018 Set 1 — Question 43
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Control Systems → Differential Equations → First-Order Equations
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Question
Consider a system governed by the following equationsThe initial conditions are such that . Let and . Which one of the following is true?
Correct answer
(C) x_(1f) = x_(2f) < ∞
Solution
1.Summing the two state equations: . This implies (constant) for all . Specifically, .
2.Subtracting the equations: .
3.Let . Then .
4.As , , which means , so .
5.From the sum conservation: .
6.Since and are finite, .
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