The stability region for Schur stable trinomials with general complex coefficients

Abstract

In this paper, we characterize the stability region for trinomials of the form $f(\zeta ):=a{\zeta }^n+b{\zeta }^m+c$, $\zeta \in \mathbb{C}$, where $a$, $b$ and $c$ are non-zero complex numbers and $n,m\in \mathbb{N}$ with $n>m$. More precisely, we provide necessary and sufficient conditions on the coefficients $a$, $b$ and $c$ in order that all the roots of the trinomial $f$ belongs to the open unit disc in the complex plane. The proof is based on Bohl's Theorem introduced in 1908.

28 pages and 2 figures