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Journals / Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik / 2000 / Cilt: 1 - Sayı: 1

Matris politoplarının değerler alanı

Field of values of matrix polytopes

A. Bülent ÖZGÜLER
Karim SAADAOUI
Pages
57–65
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

For polytopes with spectral vertex matrices, Schur stability of vertices is necessary and sufficient for the Schur stability of the polytope.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The tool of field of values (also known as the classical numerical range) is used to recover most results available in the literature and to obtain some new ones concerning Hurwitz and Schur stability of matrix polytopes.
📊
Key Findings & Data:Some facts, obtained by an application of the elementary properties of field of values are as follows.
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Conclusion & Impact:For polytopes with spectral vertex matrices, Schur stability of vertices is necessary and sufficient for the Schur stability of the polytope.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The tool of field of values (also known as the classical numerical range) is used to recover most results available in the literature and to obtain some new ones concerning Hurwitz and Schur stability of matrix polytopes. Some facts, obtained by an application of the elementary properties of field of values are as follows. If the vertex matrices have polygonal field of values, then the matrix polytope is Hurwitz and Schur stable if and only if the vertex matrices are Hurwitz and Schur stable, respectively. If the polytope is nonnegative and the symmetric part of each vertex matrix is Schur stable, then the polytope is Schur stable. For polytopes with spectral vertex matrices, Schur stability of vertices is necessary and sufficient for the Schur stability of the polytope.

Özet

Matris politoplarının Hurwitz ve Schur kararlılığı ile ilgili bilinen bir çok sonuç ve bazı yeni sonuçlar, nümerik kapsam olarak da bilinen, değerler alanı fikri kullanılarak elde edilmektedir. Bu şekilde ulaşılan bazı sonuçlar şunlardır: Eğer politop, değerler alanı poligon olan köşe matrislerinden oluşmuşsa, köşe matrislerinin Hurwitz veya Schur kararlı olması, tüm politopun kararlılığı için gerek ve yeter şarttır. Eğer politop negatif olmayan matrislerden oluşuyorsa ve köşe matrislerinin simetrik kısımları Schur kararlı ise, tüm politop da kararlıdır. Eğer politopun köşe matrisleri spektral matrislerse, köşe matrislerinin Schur kararlılığı, tüm politopun Schur kararlılığı için gerek ve yeter şarttır.

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Cite This Article

ÖZGÜLER, A. B., SAADAOUI, K. (2022). Matris politoplarının değerler alanı. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik, Cilt: 1 - Sayı: 1, 57–65. https://ajindex.com/articles/438540

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