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GATE ECE 2008 | Question-39


A certain system has transfer function $G(s)=\frac{s+8}{s^{2}+\alpha s-4}$, where $\alpha$ is a parameter. Consider the standard negative unity feedback configuration as shown below.


Which of the following statements is true?

  1. The closed loop system is never stable for any value of $\alpha$.
  2. For some positive values of $\alpha$, the closed loop system is stable, but not for all positive values.
  3. For all positive values of $\alpha$, the closed loop system is stable.
  4. The closed loop system is stable for all values of $\alpha$, both positive and negative.
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