A note on the Li\'{e}nard-Chipart criterion and roots of some families of polynomials

TL;DR

This paper introduces new inequalities offering sufficient conditions for polynomial instability, addressing complex control problems where traditional criteria are hard to apply, and discusses stability of specific degree five polynomials.

Contribution

It provides novel inequalities as alternative criteria for Hurwitz instability and explores stability of certain degree five polynomials.

Findings

New inequalities for polynomial instability conditions

Applicability to complex control problems

Analysis of degree five polynomial stability

Abstract

We present some inequalities that provide different sufficient conditions for an univariate monic polynomial to be Hurwitz unstable. These are motivated by difficult control problems where direct application of the Li\'enard-Chipart criterion is not feasible. Hurwitz stability of some polynomials of degree five is also discussed. These results may be interpreted as stability results for some interval polynomials.