A note on Hurwitz stability of matrices

Guang Ren Duan; Ron J. Patton

doi:10.1016/S0005-1098(97)00217-3

A note on Hurwitz stability of matrices

Guang Ren Duan^*
, Ron J. Patton

^*Corresponding author for this work

School of Astronautics

University of Hull

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

40 Scopus citations

Abstract

This note proves that every Hurwitz-stable matrix can be expressed as the product of a symmetric positive-definite matrix and a generalised negative-definite matrix. Based on this it is further shown that the entire set of all Hurwitz-stable matrices of order n is the product of two convex open cones and itself forms a simply connected open cone in the parameter space with a vertex at the origin.

Original language	English
Pages (from-to)	509-511
Number of pages	3
Journal	Automatica
Volume	34
Issue number	4
DOIs	https://doi.org/10.1016/S0005-1098(97)00217-3
State	Published - Apr 1998

Keywords

Convexity
Generalised positive definiteness
Hurwitz stability
Matrices
Simple connectivity

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10.1016/S0005-1098(97)00217-3

Cite this

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title = "A note on Hurwitz stability of matrices",

abstract = "This note proves that every Hurwitz-stable matrix can be expressed as the product of a symmetric positive-definite matrix and a generalised negative-definite matrix. Based on this it is further shown that the entire set of all Hurwitz-stable matrices of order n is the product of two convex open cones and itself forms a simply connected open cone in the parameter space with a vertex at the origin.",

keywords = "Convexity, Generalised positive definiteness, Hurwitz stability, Matrices, Simple connectivity",

author = "Duan, \{Guang Ren\} and Patton, \{Ron J.\}",

year = "1998",

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AU - Duan, Guang Ren

AU - Patton, Ron J.

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N2 - This note proves that every Hurwitz-stable matrix can be expressed as the product of a symmetric positive-definite matrix and a generalised negative-definite matrix. Based on this it is further shown that the entire set of all Hurwitz-stable matrices of order n is the product of two convex open cones and itself forms a simply connected open cone in the parameter space with a vertex at the origin.

AB - This note proves that every Hurwitz-stable matrix can be expressed as the product of a symmetric positive-definite matrix and a generalised negative-definite matrix. Based on this it is further shown that the entire set of all Hurwitz-stable matrices of order n is the product of two convex open cones and itself forms a simply connected open cone in the parameter space with a vertex at the origin.

KW - Convexity

KW - Generalised positive definiteness

KW - Hurwitz stability

KW - Matrices

KW - Simple connectivity

UR - https://www.scopus.com/pages/publications/0032048756

U2 - 10.1016/S0005-1098(97)00217-3

DO - 10.1016/S0005-1098(97)00217-3

M3 - 文章

AN - SCOPUS:0032048756

SN - 0005-1098

VL - 34

SP - 509

EP - 511

JO - Automatica

JF - Automatica

IS - 4

ER -

A note on Hurwitz stability of matrices

Abstract

Keywords

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