Generalized form of Hurwitz-Routh criterion and Hopf bifurcation of higher order

The Routh-Hurwitz Stability Criterion, Revisited

In the mid-nineteenth century James C. Maxwell, and others, became interested in the stability of motion of dynamic systems. Maxwell’s interest in stability stemmed in part from his work with an automatic control system a speed governor he and his colleagues were using in laboratory measurements to establish the definition of the ohm. Maxwell was the first to publish a dynamic analysis of this ...

A "simplest Possible" Property of the Generalized Routh-hurwitz Conditions*

Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations.

Elementary proof of the Routh-Hurwitz test

This note presents an elementary proof of the familiar Routh-Hurwitz test. The proof is basically one continuity argument, it does not rely on Sturm chains, Cauchy index and the principle of the argument and it is fully self-contained. In the same style an extended Routh-Hurwitz test is derived, which finds the inertia of polynomials.

Hermite–Biehler, Routh–Hurwitz, and total positivity

Simple proofs of the Hermite–Biehler and Routh–Hurwitz theorems are presented. The total nonnegativity of the Hurwitz matrix of a stable real polynomial follows as an immediate corollary. © 2003 Elsevier Inc. All rights reserved. AMS classification: 93D05; 34D99; 12D10; 26C05; 26C10; 30C15; 15A23; 15A48; 15A57