Control Theory #35 — Routh-Hurwitz Stability (Worked Example 12)

Instructor: Dr. Süleyman Burak ÇELİK

In this worked example, we apply the Routh-Hurwitz stability criterion to three transfer functions. We check properness, do a quick stability inspection, build full Routh tables, and write the pole-zero form. Topics covered: - Part (a): Properness via relative degree (deg denominator − deg numerator ≥ 0) - Part (b): Quick stability inspection from factored form - Part (c): Full Routh-Hurwitz tables for all three transfer functions - Part (d): Pole-zero representation of G2 using the quadratic formula Key results: - G1 = (s⁴+3s+2)/(s²+4s−3): improper (rd = −2), instable (1 sign change) - G2 = (5s+20)/[(s−4)(s²+2s+4)]: strictly proper (rd = 2), instable (pole at s = +4) - G3 = (s−4)/[(s+4)(s+7)]: strictly proper (rd = 1), STABLE (no sign changes) - Pole-zero form: G2(s) = 5(s+4) / [(s−4)(s+1−j√3)(s+1+j√3)] Routh-Hurwitz rule: number of sign changes in the first column equals the number of poles in the right half plane. Every step shown clearly — no shortcuts. Playlist: Control Theory - AcEdumy GitHub: https://github.com/acedumy #ControlTheory #WorkedExample #RouthHurwitz #Stability #TransferFunction #ControlEngineering #PoleZero #AcEdumy