Routh-Hurwitz-criterium I

Consider an electrical power grid, where stability is crucial to prevent blackouts. Using the Routh-Hurwitz criterion, the system's stability under varying load conditions or faults can be assessed.

Consider a closed-loop transfer function. To create a Routh table, the rows are labeled with powers of s from the highest.

The first row is populated horizontally with every other coefficient of the denominator, starting with the highest power. The second row follows the next highest power and lists the skipped coefficients.

Subsequent entries are calculated through negative determinants of preceding rows, divided by the directly above first-column entry.

For a system, Routh table rows are computed. Positive constant scales rows independently.

The Routh-Hurwitz criterion states that the number of roots of the polynomial in the right half-plane equals the number of sign changes in the first column of the Routh table, indicating an unstable system.

A system is stable if all poles are in the left half of the s-plane, which equates to no sign changes in the first column of the Routh table.