The stability region for Schur stable trinomials with general complex coefficients

Autor:	Barrera, Gerardo, Barrera, Waldemar, Navarrete, Juan Pablo
Rok vydání:	2023
Předmět:	Mathematics - Complex Variables Mathematics - Classical Analysis and ODEs Mathematics - Dynamical Systems Primary 12D10 26C10 30C15 Secondary 93D23 11B37
Zdroj:	Journal of Dynamics and Differential Equations 2023
Druh dokumentu:	Working Paper
DOI:	10.1007/s10884-023-10331-w
Popis:	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. Comment: 28 pages and 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.09147 Zobrazit plný text záznamu View this record from Arxiv