Necessary conditions for the stability of polynomials and their use (Q1922455)

The aim of the paper is to propose a unified technique for deriving stability criteria. More precisely, classical results of Gauss and Newton are used to derive criteria for testing whether a polynomial with real or complex coefficients is Hurwitz, aperiodic, and sector stable. The obtained results can be used to estimate the probability that a random polynomial is a Hurwitz polynomial and to study the stability of a discrete system. Simple necessary conditions allow to solve certain robust stability problems without any computations. The standard fractional-linear transformation can be applied and the Schur stability can be replaced by the study of Hurwitz stability.