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Let G(s) = 1/((s+1)(s+2)). Then the closed-loop system shown in the figure below is

1. stable for all K > 2.
2. unstable for all K > 2.
3. unstable for all K > 1.
4. stable for all K > 1.

Correct answer: stable for all K > 1.

Solution

The closed-loop system is stable for all K > 1 because the poles of the characteristic equation move to the left half of the s-plane as K increases, ensuring that the system remains stable.

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