Routh, Hurwitz, Bieler and Kharitonov: A unified approach using the Schwarz form

Abstract

The equivalence of the well known Routh and Hurwitz criteria and the conditions derived using a quadratic Lyapunov function, were established by Patrick Parks. In this paper it is shown that the basic mathematical framework used by him involving the Schwarz form can be used to derive the same stability conditions in a simple form, and that results due to Bieler and Kharitonov can also be derived in a unified fashion. © 2013 AACC American Automatic Control Council.