On a Specialised Case of the Routh-Hurwitz Stability Criteria

Summary The well-known Routh-Hurwitz stability criteria apply to polynomial characteristic equations with real coefficients. Lesser known criteria were devised by Hurwitz for the case of polynomials with complex coefficients. However, when polynomials with real coefficients and even powers only are directly subjected to the first-mentioned criteria, all the test determinants obtained vanish identically and thus fail to indicate the state of stability. In the present paper, the stability test functions for such characteristic polynomials are derived.