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arXiv · 2304.09147

The stability region for Schur stable trinomials with general complex coefficients

Gerardo Barrera·Waldemar Barrera·Juan Pablo Navarrete
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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.

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Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete. 2023-04-18. The stability region for Schur stable trinomials with general complex coefficients. https://doi.org/10.1007/s10884-023-10331-w

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