Topic: Control Systems
Characteristic equation of $H(s)$ is given as $3s^4+2s^3+5s^2+s+2=0$ is
- A. unstable
- B. stable
- C. all poles in right half plane
- D. unstable with only one pole in right half plane
Answer: A. unstable
Explanation: Applying the Routh-Hurwitz criterion to the polynomial $3s^4+2s^3+5s^2+s+2=0$, the first column of the Routh array evaluates to 3, 2, 3.5, -0.443, and 2. Since there are two sign changes (from positive to negative and back to positive), there are two poles in the right half of the s-plane, making the system unstable.