Activity #8
Routh-Hurwitz criterion for stability
1. Make a Routh table and tell how many roots of the following polynomial are in the
right half plane and in the left half plane:
𝑃(𝑠) = 3𝑠 7 + 9𝑠 6 + 6𝑠 5 + 4𝑠 4 + 7𝑠 3 + 8𝑠 2 + 2𝑠 + 6
2. Given the following system, find the ranges of “K” for stability using the RouthHurwitz criterion:
3. Use the Routh-Hurwitz criterion to find how many poles of the following closedloop system, 𝑇(𝑠), are in the rhp, in the lhp, and on the jω-axis:
𝑇(𝑠) =
𝑠 3 + 7𝑠 2 − 21𝑠 + 10
𝑠 6 + 𝑠 5 − 6𝑠 4 − 𝑠 2 − 𝑠 + 6
4. Use the Routh-Hurwitz criterion to find the number of poles in the left half-plane,
the right half-plane, and on the jω-axis for the system: