Question:

The system \( G(s) = \frac{0.8}{s^2 + s - 2} \) is subjected to a step input. The system output \( y(t) \) as \( t \rightarrow \infty \) is:

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If the system has a pole with positive real part, the output will be unbounded.
Updated On: June 02, 2025
  • 0.8
  • 0.4
  • -0.4
  • unbounded
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The Correct Option is D

Solution and Explanation

The given transfer function has a pole on the right-hand side of the s-plane (since the characteristic equation \( s^2 + s - 2 = 0 \) has a root at \( s = 1 \)), indicating the system is unstable. As a result, the step response of the system grows without bound as \( t \to \infty \).
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