23.7 : ラウス・ハーウィッツ基準 II

In the Routh-Hurwitz criterion, two distinct situations can occur.

When a singular zero exclusively appears in the Routh table's first column, it raises the division by zero issue.

To circumvent this problem, a small number, usually epsilon, replaces the zero.

The interpretation begins by assuming a sign for epsilon. If epsilon is chosen to be positive, the sign change indicates that the system is unstable with two poles in the right half-plane. Similarly, choosing a negative leads to the same conclusion of instability.

The second scenario occurs when an entire row comprises solely zeros. This suggests that an even polynomial is a factor of the original polynomial.

An auxiliary polynomial is formed using the coefficients from the row above the zero row. This is differentiated, and the coefficients from this derivative replace the zeros in the table.

Furthermore, the usual method to construct the remaining Routh table is implemented.

Even and odd polynomials are tabulated separately, and the total number of right-half-plane poles is the sum of those found in the even and odd polynomial tables.