rouTh

Routh is a surname and a place name. The most noted bearer in mathematical history is Edward John Routh (1831–1907), a British mathematician and physicist who made significant contributions to dynamical systems and stability analysis. Routh is best known for developing the Routh array, a tabular method used to assess the stability of a polynomial without computing its roots. The method was later extended by others and is often discussed in the context of the Routh–Hurwitz stability criterion.

In control theory and engineering, the Routh‑Hurwitz stability criterion provides a practical test to determine whether all roots of a linear time‑invariant system's characteristic polynomial lie in the left half of the complex plane, which corresponds to a stable system. The criterion is evaluated using the Routh array; the system is stable if and only if the first column of the array has no sign changes (and, when zeros occur, certain regularization procedures are applied).

Routh also refers to a village and civil parish in England. The name appears in other contexts, including surnames and historical references to mathematicians and engineers.