Topic: Control Systems
The following system $\frac{4s+1}{4s^{2}+1}$ is
- A. Unstable
- B. Stable
- C. Marginally stable
- D. Stability can't be determined
Answer: C. Marginally stable
Explanation: The stability of a system is determined by the poles of its transfer function, which are the roots of the characteristic equation (denominator = 0).
$4s^2 + 1 = 0 \Rightarrow 4s^2 = -1 \Rightarrow s^2 = -\frac{1}{4} \Rightarrow s = \pm j0.5$.
The poles lie purely on the imaginary axis ($j\omega$-axis) and are non-repeated. Therefore, the system is marginally stable.