The stability region for Schur stable trinomials with general complex coefficients
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914775633494016 |
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| author | Barrera, Gerardo Barrera, Waldemar Navarrete, Juan Pablo |
| author_facet | Barrera, Gerardo Barrera, Waldemar Navarrete, Juan Pablo |
| contents | In this paper, we characterize the stability region for trinomials of the form $f(ζ):=aζ^n + bζ^m +c$, $ζ\in \mathbb{C}$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_09147 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The stability region for Schur stable trinomials with general complex coefficients Barrera, Gerardo Barrera, Waldemar Navarrete, Juan Pablo Complex Variables Classical Analysis and ODEs Dynamical Systems Primary 12D10, 26C10, 30C15, Secondary 93D23, 11B37 In this paper, we characterize the stability region for trinomials of the form $f(ζ):=aζ^n + bζ^m +c$, $ζ\in \mathbb{C}$, 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. |
| title | The stability region for Schur stable trinomials with general complex coefficients |
| topic | Complex Variables Classical Analysis and ODEs Dynamical Systems Primary 12D10, 26C10, 30C15, Secondary 93D23, 11B37 |
| url | https://arxiv.org/abs/2304.09147 |