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:

• A. 0.8
• B. 0.4
• C. -0.4
• D. unbounded

Hint:

If the system has a pole with positive real part, the output will be unbounded.

Answer 1

The Correct Option is D

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 \( t \to \infty \).