The Routh and Routh‐Hurwitz Stability Criteria

THE classic Routh stability criteria1 are applicable only to polynomial characteristic equations with real coefficients. The writer recently came across co‐related criteria in a Russian treatise2 on the stability of rotating shafts which criteria are applicable to polynomial equations with complex coefficients. These criteria were apparently devised by Hurwitz as extensions of the Routh criteria and are thus known as Routh‐Hurwitz stability criteria. They are, however, not well known to British students of stability analysis nor are they readily accessible in British publications.