Topic: Control Systems
For a standard second order polynomial given by $G(s)=a_{2}s^{2}+a_{1}s+a_{0}$, according to the Routh test, the stability criterion is given by
- A. $a_{2}>0, a_{1}>0, a_{0}>0$
- B. $a_{2}<0, a_{1}<0, a_{0}<0$
- C. $a_{2}>0, a_{1}>0, a_{0}<0$
- D. $a_{2}<0, a_{1}>0, a_{0}>0$
Answer: A. $a_{2}>0, a_{1}>0, a_{0}>0$
Explanation: According to the Routh-Hurwitz stability criterion, a necessary condition for a system to be strictly stable (all roots in the left half of the s-plane) is that all coefficients of its characteristic polynomial must be strictly positive and non-zero (assuming the highest degree term is chosen positive). Therefore, $a_2 > 0$, $a_1 > 0$, and $a_0 > 0$.