# Test Stability using Routh Stability Method

1. ### mym786

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.

2. ### CEL

639
i + G(s)H(s) = 0 means:
$$s^3+\alpha s^2 + 1 = 0$$
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.

3. ### mym786

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.