On the nearest stable 2 x 2 matrix, dedicated to prof. sze-bi hsu in appreciation of his inspiring ideas

Yueh Cheng Kuo; Huan Chang Cheng; Jhih You Syu; Shih Feng Shieh

doi:10.3934/dcdsb.2020358

On the nearest stable 2 x 2 matrix, dedicated to prof. sze-bi hsu in appreciation of his inspiring ideas

Yueh Cheng Kuo
, Huan Chang Cheng
, Jhih You Syu
, Shih Feng Shieh^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the continuous-time nearest stable matrixproblem: Given a 2x2 real matrix A, minimize the Frobenius norm of A-X, where X is a stable matrix. We provide an explicit formula for the global minimizer X*. The uniqueness of the minimizer is also studied.

Original language	English
Pages (from-to)	2025-2035
Number of pages	11
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	26
Issue number	4
DOIs	https://doi.org/10.3934/dcdsb.2020358
Publication status	Published - 2021 Apr

Keywords

Global minimizer
Linear continuous-time systems
Matrix approximation
Stability ra- dius

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdsb.2020358

Cite this

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title = "On the nearest stable 2 x 2 matrix, dedicated to prof. sze-bi hsu in appreciation of his inspiring ideas",

abstract = "In this paper, we study the continuous-time nearest stable matrixproblem: Given a 2x2 real matrix A, minimize the Frobenius norm of A-X, where X is a stable matrix. We provide an explicit formula for the global minimizer X*. The uniqueness of the minimizer is also studied.",

keywords = "Global minimizer, Linear continuous-time systems, Matrix approximation, Stability ra- dius",

author = "Kuo, \{Yueh Cheng\} and Cheng, \{Huan Chang\} and Syu, \{Jhih You\} and Shieh, \{Shih Feng\}",

year = "2021",

month = apr,

doi = "10.3934/dcdsb.2020358",

language = "English",

volume = "26",

pages = "2025--2035",

journal = "Discrete and Continuous Dynamical Systems - Series B",

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AU - Cheng, Huan Chang

AU - Syu, Jhih You

AU - Shieh, Shih Feng

PY - 2021/4

Y1 - 2021/4

N2 - In this paper, we study the continuous-time nearest stable matrixproblem: Given a 2x2 real matrix A, minimize the Frobenius norm of A-X, where X is a stable matrix. We provide an explicit formula for the global minimizer X*. The uniqueness of the minimizer is also studied.

AB - In this paper, we study the continuous-time nearest stable matrixproblem: Given a 2x2 real matrix A, minimize the Frobenius norm of A-X, where X is a stable matrix. We provide an explicit formula for the global minimizer X*. The uniqueness of the minimizer is also studied.

KW - Global minimizer

KW - Linear continuous-time systems

KW - Matrix approximation

KW - Stability ra- dius

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UR - https://www.scopus.com/pages/publications/85101412117#tab=citedBy

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IS - 4

ER -

On the nearest stable 2 x 2 matrix, dedicated to prof. sze-bi hsu in appreciation of his inspiring ideas

Abstract

Keywords

ASJC Scopus subject areas

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