# Test Stability using Routh Stability Method

by mym786
Tags: method, routh, stability, test
 P: 11 1. The problem statement, all variables and given/known data For a control system that has G(s)H(s) = $\frac{1}{s^{2}*(s+\alpha)}$ 2. Relevant equations 1 + G(s)H(s) = 0 3. The attempt at a solution Exam question i messed up . I really need to know the answer.
 Quote by mym786 1. The problem statement, all variables and given/known data For a control system that has G(s)H(s) = $\frac{1}{s^{2}*(s+\alpha)}$ 2. Relevant equations 1 + G(s)H(s) = 0 3. The attempt at a solution Exam question i messed up . I really need to know the answer.
$$s^3+\alpha s^2 + 1 = 0$$
Since the polynomial is incomplete (there is no term in $$s^1$$) there is at least one root in the RHP and the system is unstable. No need to use Routh algorithm.
 P: 11 I forgot one more thing. It also says find the value of $\alpha$ for which the system can be classified in the critically stable state.