New reductions of Hurwitz determinants

Abstract

Two lesser-known classical elimination techniques are applied in matrix form to the linear system stability problem of determining when the roots of a real nth degree polynomial all have negative real parts. In particular, for calculation of the critical Hurwitz determinant Δ n−1 a new tabular scheme is obtained which is superior to the Routh array for parametric stability problems. An extension leads to new half-order expressions for the other Δt Another reduction of Δ−1 in terms of minors of order about ¼n is also given.