Open Problems Related to the Hurwitz Stability of Polynomials Segments

Aguirre-Hernandez Baltazar; Ricardo Garcia-Sosa Faustino; Arturo Loredo-Villalobos Carlos; Villafuerte-Segura Raul; Campos-Canton Eric

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Open Problems Related to the Hurwitz Stability of Polynomials Segments

机译：与多项式段的Hurwitz稳定性有关的开放问题

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In the framework of robust stability analysis of linear systems, the development of techniques and methods that help to obtain necessary and sufficient conditions to determine stability of convex combinations of polynomials is paramount. In this paper, knowing that Hurwitz polynomials set is not a convex set, a brief overview of some results and open problems concerning the stability of the convex combinations of Hurwitz polynomials is then provided.

机译：在线性系统鲁棒稳定性分析的框架中，帮助获得确定多项式凸组合稳定性的必要和充分条件的技术和方法的发展至关重要。在了解Hurwitz多项式集不是凸集的情况下，本文简要概述了一些结果以及有关Hurwitz多项式凸集稳定性的开放问题。

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《Mathematical Problems in Engineering》 |2018年第2期|2075903.1-2075903.8|共8页
作者
Aguirre-Hernandez Baltazar; Ricardo Garcia-Sosa Faustino; Arturo Loredo-Villalobos Carlos; Villafuerte-Segura Raul; Campos-Canton Eric;
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Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, San Rafael Atlixco 186, Ciudad De Mexico 09340, Mexico;

Inst Politecn Nacl, SEPI UPIICSA, Ciudad De Mexico 08400, Mexico;

Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, San Rafael Atlixco 186, Ciudad De Mexico 09340, Mexico;

Hidalgo State Univ, Res Ctr Informat Technol & Syst, Pachuca, Hgo, Mexico;

IPICyT, Div Matemat Aplicadas, San Luis Potosi 78216, Slp, Mexico;

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1. Open Problems Related to the Hurwitz Stability of Polynomials Segments [J] . Baltazar Aguirre-Hernndez, Faustino Ricardo Garca-Sosa, Carlos Arturo Loredo-Villalobos, Mathematical Problems in Engineering: Theory, Methods and Applications . 2018,第5期

机译：与多项式分段的Hurwitz稳定性有关的开放问题
2. Open Problems Related to the Hurwitz Stability of Polynomials Segments [J] . Baltazar Aguirre-Hernndez, Faustino Ricardo Garca-Sosa, Carlos Arturo Loredo-Villalobos, Mathematical Problems in Engineering: Theory, Methods and Applications . 2018,第2期

机译：与多项式分段的Hurwitz稳定性有关的开放问题
3. Properties of the entire set of Hurwitz polynomials and stability analysis of polynomial families [J] . Guang-Ren Duan, Min-Zhi Wang IEEE Transactions on Automatic Control . 1994,第12期

机译：整套Hurwitz多项式的性质和多项式族的稳定性分析
4. On quadratic Hurwitz stability of segment polynomials [C] . Kokame, H., Mori, . 1998

机译：段多项式的二次Hurwitz稳定性
5. Hurwitz quaternion valued polynomials and their denominators . [D] . Pavlovski, Mark. 2010

机译：Hurwitz四元数多项式及其分母。
6. A Segmental Polynomial Model of Ventricular Electrograms as a Simple and Efficient Morphology Discriminator for Implantable Devices [O] . Jeffrey L. Williams, Vladimir Shusterman, Samir Saba 2006

机译：心电图的分段多项式模型作为一种简单高效的可植入设备形态识别器
7. Hurwitz Stability of Matrix Segment and The Common Solution Set of 2 and 3-Dimensional Lyapunov Equations [O] . Şerife YILMAZ 2020

机译：矩阵段的Hurwitz稳定性和2和3维Lyapunov方程的共同解决方案组
8. On the representation of the stability region in oscillation problems with the aid of the Hurwitz determinants [R] . Sponder, E W 1952

机译：借助Hurwitz行列式研究振动问题中稳定区域的表示

Open Problems Related to the Hurwitz Stability of Polynomials Segments

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