Week 06
Routh-Hurwitz Stability
I follow the saved course materials and calculations from modeling through stability, root locus, and frequency response.
What I connect in this unit
A Routh-Hurwitz array determines the number of right-half-plane poles directly from the characteristic-polynomial coefficients. Sign changes in the first column reveal instability, and a symbolic gain turns the same conditions into an admissible gain interval.
Concept map
- Characteristic equation
- Routh arrays
- Right-half-plane poles
- Gain range
Technical anchor
Place alternating coefficients of a_n s^n+...+a_0=0 in the first two rows and complete the first column. Solve all first-column positivity inequalities together to obtain the gain condition.
How I review it
Treat a zero leading element separately from an all-zero row, and use the auxiliary polynomial to check for imaginary-axis roots at a boundary gain.
Connection to the full course
Unit 6 of 12. Unit numbers organize the concepts found in the materials and do not reproduce an attendance schedule.